/*******************************************************************************
 * This file is part of SWIFT.
 * Copyright (c) 2016 Matthieu Schaller (matthieu.schaller@durham.ac.uk) &
 *                    Josh Borrow (joshua.borrow@durham.ac.uk)
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published
 * by the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 *
 ******************************************************************************/
#ifndef SWIFT_ANARCHY_PU_HYDRO_H
#define SWIFT_ANARCHY_PU_HYDRO_H

/**
 * @file AnarchyPU/hydro.h
 * @brief P-U conservative implementation of SPH,
 *        with added ANARCHY physics (Cullen & Denhen 2011 AV,
 *        Price 2008 thermal diffusion (Non-neighbour loop
 *        equations)
 *
 * This implementation corresponds to the one presented in the SWIFT
 * documentation and in Hopkins, "A general class of Lagrangian smoothed
 * particle hydrodynamics methods and implications for fluid mixing problems",
 * MNRAS, 2013.
 */

#include "adiabatic_index.h"
#include "approx_math.h"
#include "cosmology.h"
#include "dimension.h"
#include "entropy_floor.h"
#include "equation_of_state.h"
#include "hydro_properties.h"
#include "hydro_space.h"
#include "kernel_hydro.h"
#include "minmax.h"

#include "./hydro_parameters.h"

#include <float.h>

/**
 * @brief Returns the comoving internal energy of a particle at the last
 * time the particle was kicked.
 *
 * For implementations where the main thermodynamic variable
 * is not internal energy, this function computes the internal
 * energy from the thermodynamic variable.
 *
 * @param p The particle of interest
 * @param xp The extended data of the particle of interest.
 */
__attribute__((always_inline)) INLINE static float
hydro_get_comoving_internal_energy(const struct part *restrict p,
                                   const struct xpart *restrict xp) {

  return xp->u_full;
}

/**
 * @brief Returns the physical internal energy of a particle at the last
 * time the particle was kicked.
 *
 * For implementations where the main thermodynamic variable
 * is not internal energy, this function computes the internal
 * energy from the thermodynamic variable and converts it to
 * physical coordinates.
 *
 * @param p The particle of interest.
 * @param xp The extended data of the particle of interest.
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static float
hydro_get_physical_internal_energy(const struct part *restrict p,
                                   const struct xpart *restrict xp,
                                   const struct cosmology *cosmo) {

  return xp->u_full * cosmo->a_factor_internal_energy;
}

/**
 * @brief Returns the comoving internal energy of a particle drifted to the
 * current time.
 *
 * @param p The particle of interest
 */
__attribute__((always_inline)) INLINE static float
hydro_get_drifted_comoving_internal_energy(const struct part *restrict p) {

  return p->u;
}

/**
 * @brief Returns the physical internal energy of a particle drifted to the
 * current time.
 *
 * @param p The particle of interest.
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static float
hydro_get_drifted_physical_internal_energy(const struct part *restrict p,
                                           const struct cosmology *cosmo) {

  return p->u * cosmo->a_factor_internal_energy;
}

/**
 * @brief Returns the comoving pressure of a particle
 *
 * Computes the pressure based on the particle's properties.
 *
 * @param p The particle of interest
 */
__attribute__((always_inline)) INLINE static float hydro_get_comoving_pressure(
    const struct part *restrict p) {

  return p->pressure_bar;
}

/**
 * @brief Returns the physical pressure of a particle
 *
 * Computes the pressure based on the particle's properties and
 * convert it to physical coordinates.
 *
 * @param p The particle of interest
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static float hydro_get_physical_pressure(
    const struct part *restrict p, const struct cosmology *cosmo) {

  return cosmo->a_factor_pressure * p->pressure_bar;
}

/**
 * @brief Returns the comoving entropy of a particle at the last
 * time the particle was kicked.
 *
 * For implementations where the main thermodynamic variable
 * is not entropy, this function computes the entropy from
 * the thermodynamic variable.
 *
 * @param p The particle of interest
 * @param xp The extended data of the particle of interest.
 */
__attribute__((always_inline)) INLINE static float hydro_get_comoving_entropy(
    const struct part *restrict p, const struct xpart *restrict xp) {

  return gas_entropy_from_internal_energy(p->rho, xp->u_full);
}

/**
 * @brief Returns the physical entropy of a particle at the last
 * time the particle was kicked.
 *
 * For implementations where the main thermodynamic variable
 * is not entropy, this function computes the entropy from
 * the thermodynamic variable and converts it to
 * physical coordinates.
 *
 * @param p The particle of interest.
 * @param xp The extended data of the particle of interest.
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static float hydro_get_physical_entropy(
    const struct part *restrict p, const struct xpart *restrict xp,
    const struct cosmology *cosmo) {

  /* Note: no cosmological conversion required here with our choice of
   * coordinates. */
  return gas_entropy_from_internal_energy(p->rho, xp->u_full);
}

/**
 * @brief Returns the comoving entropy of a particle drifted to the
 * current time.
 *
 * @param p The particle of interest.
 */
__attribute__((always_inline)) INLINE static float
hydro_get_drifted_comoving_entropy(const struct part *restrict p) {

  return gas_entropy_from_internal_energy(p->rho, p->u);
}

/**
 * @brief Returns the physical entropy of a particle drifted to the
 * current time.
 *
 * @param p The particle of interest.
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static float
hydro_get_drifted_physical_entropy(const struct part *restrict p,
                                   const struct cosmology *cosmo) {

  /* Note: no cosmological conversion required here with our choice of
   * coordinates. */
  return gas_entropy_from_internal_energy(p->rho, p->u);
}

/**
 * @brief Returns the comoving sound speed of a particle
 *
 * @param p The particle of interest
 */
__attribute__((always_inline)) INLINE static float
hydro_get_comoving_soundspeed(const struct part *restrict p) {

  /* Compute the sound speed -- see theory section for justification */
  /* IDEAL GAS ONLY -- P-U does not work with generic EoS. */

  const float square_rooted = sqrtf(hydro_gamma * p->pressure_bar / p->rho);

  return square_rooted;
}

/**
 * @brief Returns the physical sound speed of a particle
 *
 * @param p The particle of interest
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static float
hydro_get_physical_soundspeed(const struct part *restrict p,
                              const struct cosmology *cosmo) {

  return cosmo->a_factor_sound_speed * hydro_get_comoving_soundspeed(p);
}

/**
 * @brief Returns the comoving density of a particle
 *
 * @param p The particle of interest
 */
__attribute__((always_inline)) INLINE static float hydro_get_comoving_density(
    const struct part *restrict p) {

  return p->rho;
}

/**
 * @brief Returns the comoving density of a particle.
 *
 * @param p The particle of interest
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static float hydro_get_physical_density(
    const struct part *restrict p, const struct cosmology *cosmo) {

  return cosmo->a3_inv * p->rho;
}

/**
 * @brief Returns the mass of a particle
 *
 * @param p The particle of interest
 */
__attribute__((always_inline)) INLINE static float hydro_get_mass(
    const struct part *restrict p) {

  return p->mass;
}

/**
 * @brief Sets the mass of a particle
 *
 * @param p The particle of interest
 * @param m The mass to set.
 */
__attribute__((always_inline)) INLINE static void hydro_set_mass(
    struct part *restrict p, float m) {

  p->mass = m;
}

/**
 * @brief Returns the velocities drifted to the current time of a particle.
 *
 * @param p The particle of interest
 * @param xp The extended data of the particle.
 * @param dt_kick_hydro The time (for hydro accelerations) since the last kick.
 * @param dt_kick_grav The time (for gravity accelerations) since the last kick.
 * @param v (return) The velocities at the current time.
 */
__attribute__((always_inline)) INLINE static void hydro_get_drifted_velocities(
    const struct part *restrict p, const struct xpart *xp, float dt_kick_hydro,
    float dt_kick_grav, float v[3]) {

  v[0] = xp->v_full[0] + p->a_hydro[0] * dt_kick_hydro +
         xp->a_grav[0] * dt_kick_grav;
  v[1] = xp->v_full[1] + p->a_hydro[1] * dt_kick_hydro +
         xp->a_grav[1] * dt_kick_grav;
  v[2] = xp->v_full[2] + p->a_hydro[2] * dt_kick_hydro +
         xp->a_grav[2] * dt_kick_grav;
}

/**
 * @brief Returns the time derivative of internal energy of a particle
 *
 * We assume a constant density.
 *
 * @param p The particle of interest
 */
__attribute__((always_inline)) INLINE static float
hydro_get_comoving_internal_energy_dt(const struct part *restrict p) {

  return p->u_dt;
}

/**
 * @brief Returns the time derivative of internal energy of a particle
 *
 * We assume a constant density.
 *
 * @param p The particle of interest
 * @param cosmo Cosmology data structure
 */
__attribute__((always_inline)) INLINE static float
hydro_get_physical_internal_energy_dt(const struct part *restrict p,
                                      const struct cosmology *cosmo) {

  return p->u_dt * cosmo->a_factor_internal_energy;
}

/**
 * @brief Sets the time derivative of internal energy of a particle
 *
 * We assume a constant density.
 *
 * @param p The particle of interest.
 * @param du_dt The new time derivative of the internal energy.
 */
__attribute__((always_inline)) INLINE static void
hydro_set_comoving_internal_energy_dt(struct part *restrict p, float du_dt) {

  p->u_dt = du_dt;
}

/**
 * @brief Returns the time derivative of internal energy of a particle
 *
 * We assume a constant density.
 *
 * @param p The particle of interest.
 * @param cosmo Cosmology data structure
 * @param du_dt The new time derivative of the internal energy.
 */
__attribute__((always_inline)) INLINE static void
hydro_set_physical_internal_energy_dt(struct part *restrict p,
                                      const struct cosmology *cosmo,
                                      float du_dt) {

  p->u_dt = du_dt / cosmo->a_factor_internal_energy;
}

/**
 * @brief Sets the physical entropy of a particle
 *
 * @param p The particle of interest.
 * @param xp The extended particle data.
 * @param cosmo Cosmology data structure
 * @param entropy The physical entropy
 */
__attribute__((always_inline)) INLINE static void hydro_set_physical_entropy(
    struct part *p, struct xpart *xp, const struct cosmology *cosmo,
    const float entropy) {

  /* Note there is no conversion from physical to comoving entropy */
  const float comoving_entropy = entropy;
  xp->u_full = gas_internal_energy_from_entropy(p->rho, comoving_entropy);
}

/**
 * @brief Sets the physical internal energy of a particle
 *
 * @param p The particle of interest.
 * @param xp The extended particle data.
 * @param cosmo Cosmology data structure
 * @param u The physical internal energy
 */
__attribute__((always_inline)) INLINE static void
hydro_set_physical_internal_energy(struct part *p, struct xpart *xp,
                                   const struct cosmology *cosmo,
                                   const float u) {

  xp->u_full = u / cosmo->a_factor_internal_energy;
}

/**
 * @brief Sets the drifted physical internal energy of a particle
 *
 * @param p The particle of interest.
 * @param cosmo Cosmology data structure
 * @param u The physical internal energy
 */
__attribute__((always_inline)) INLINE static void
hydro_set_drifted_physical_internal_energy(struct part *p,
                                           const struct cosmology *cosmo,
                                           const float u) {

  p->u = u / cosmo->a_factor_internal_energy;

  /* Now recompute the extra quantities */

  /* Compute the sound speed */
  const float soundspeed = hydro_get_comoving_soundspeed(p);

  /* Update variables. */
  p->force.soundspeed = soundspeed;
}

/**
 * @brief Update the value of the viscosity alpha for the scheme.
 *
 * @param p the particle of interest
 * @param alpha the new value for the viscosity coefficient.
 */
__attribute__((always_inline)) INLINE static void hydro_set_viscosity_alpha(
    struct part *restrict p, float alpha) {
  p->viscosity.alpha = alpha;
}

/**
 * @brief Update the value of the viscosity alpha to the
 *        feedback reset value for the scheme.
 *
 * @param p the particle of interest
 */
__attribute__((always_inline)) INLINE static void
hydro_set_viscosity_alpha_max_feedback(struct part *restrict p) {
  hydro_set_viscosity_alpha(p,
                            hydro_props_default_viscosity_alpha_feedback_reset);
}

/**
 * @brief Computes the hydro time-step of a given particle
 *
 * This function returns the time-step of a particle given its hydro-dynamical
 * state. A typical time-step calculation would be the use of the CFL condition.
 *
 * @param p Pointer to the particle data
 * @param xp Pointer to the extended particle data
 * @param hydro_properties The SPH parameters
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static float hydro_compute_timestep(
    const struct part *restrict p, const struct xpart *restrict xp,
    const struct hydro_props *restrict hydro_properties,
    const struct cosmology *restrict cosmo) {

  const float CFL_condition = hydro_properties->CFL_condition;

  /* CFL condition */
  const float dt_cfl = 2.f * kernel_gamma * CFL_condition * cosmo->a * p->h /
                       (cosmo->a_factor_sound_speed * p->viscosity.v_sig);

  const float dt_u_change =
      (p->u_dt != 0.0f) ? fabsf(const_max_u_change * p->u / p->u_dt) : FLT_MAX;

  return fminf(dt_cfl, dt_u_change);
}

/**
 * @brief Does some extra hydro operations once the actual physical time step
 * for the particle is known.
 *
 * @param p The particle to act upon.
 * @param dt Physical time step of the particle during the next step.
 */
__attribute__((always_inline)) INLINE static void hydro_timestep_extra(
    struct part *p, float dt) {}

/**
 * @brief Operations performed when a particle gets removed from the
 * simulation volume.
 *
 * @param p The particle.
 * @param xp The extended particle data.
 */
__attribute__((always_inline)) INLINE static void hydro_remove_part(
    const struct part *p, const struct xpart *xp) {}

/**
 * @brief Prepares a particle for the density calculation.
 *
 * Zeroes all the relevant arrays in preparation for the sums taking place in
 * the various density loop over neighbours. Typically, all fields of the
 * density sub-structure of a particle get zeroed in here.
 *
 * @param p The particle to act upon
 * @param hs #hydro_space containing hydro specific space information.
 */
__attribute__((always_inline)) INLINE static void hydro_init_part(
    struct part *restrict p, const struct hydro_space *hs) {

  p->density.wcount = 0.f;
  p->density.wcount_dh = 0.f;
  p->rho = 0.f;
  p->density.rho_dh = 0.f;
  p->pressure_bar = 0.f;
  p->density.pressure_bar_dh = 0.f;

  p->density.rot_v[0] = 0.f;
  p->density.rot_v[1] = 0.f;
  p->density.rot_v[2] = 0.f;

  p->viscosity.div_v = 0.f;
  p->diffusion.laplace_u = 0.f;
}

/**
 * @brief Finishes the density calculation.
 *
 * Multiplies the density and number of neighbours by the appropiate constants
 * and add the self-contribution term.
 * Additional quantities such as velocity gradients will also get the final
 * terms added to them here.
 *
 * Also adds/multiplies the cosmological terms if need be.
 *
 * @param p The particle to act upon
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static void hydro_end_density(
    struct part *restrict p, const struct cosmology *cosmo) {

  /* Some smoothing length multiples. */
  const float h = p->h;
  const float h_inv = 1.0f / h;                       /* 1/h */
  const float h_inv_dim = pow_dimension(h_inv);       /* 1/h^d */
  const float h_inv_dim_plus_one = h_inv_dim * h_inv; /* 1/h^(d+1) */

  /* Final operation on the density (add self-contribution). */
  p->rho += p->mass * kernel_root;
  p->density.rho_dh -= hydro_dimension * p->mass * kernel_root;
  p->pressure_bar += p->mass * p->u * kernel_root;
  p->density.pressure_bar_dh -= hydro_dimension * p->mass * p->u * kernel_root;
  p->density.wcount += kernel_root;
  p->density.wcount_dh -= hydro_dimension * kernel_root;

  /* Finish the calculation by inserting the missing h-factors */
  p->rho *= h_inv_dim;
  p->density.rho_dh *= h_inv_dim_plus_one;
  p->pressure_bar *= (h_inv_dim * hydro_gamma_minus_one);
  p->density.pressure_bar_dh *= (h_inv_dim_plus_one * hydro_gamma_minus_one);
  p->density.wcount *= h_inv_dim;
  p->density.wcount_dh *= h_inv_dim_plus_one;

  const float rho_inv = 1.f / p->rho;
  const float a_inv2 = cosmo->a2_inv;

  /* Finish calculation of the velocity curl components */
  p->density.rot_v[0] *= h_inv_dim_plus_one * a_inv2 * rho_inv;
  p->density.rot_v[1] *= h_inv_dim_plus_one * a_inv2 * rho_inv;
  p->density.rot_v[2] *= h_inv_dim_plus_one * a_inv2 * rho_inv;

  /* Finish calculation of the velocity divergence */
  p->viscosity.div_v *= h_inv_dim_plus_one * rho_inv * a_inv2;
  p->viscosity.div_v += cosmo->H * hydro_dimension;
}

/**
 * @brief Prepare a particle for the gradient calculation.
 *
 * This function is called after the density loop and before the gradient loop.
 *
 * We use it to set the physical timestep for the particle and to copy the
 * actual velocities, which we need to boost our interfaces during the flux
 * calculation. We also initialize the variables used for the time step
 * calculation.
 *
 * @param p The particle to act upon.
 * @param xp The extended particle data to act upon.
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static void hydro_prepare_gradient(
    struct part *restrict p, struct xpart *restrict xp,
    const struct cosmology *cosmo) {

  const float fac_B = cosmo->a_factor_Balsara_eps;

  /* Compute the norm of the curl */
  const float curl_v = sqrtf(p->density.rot_v[0] * p->density.rot_v[0] +
                             p->density.rot_v[1] * p->density.rot_v[1] +
                             p->density.rot_v[2] * p->density.rot_v[2]);

  /* Compute the norm of div v */
  const float abs_div_v = fabsf(p->viscosity.div_v);

  /* Compute the sound speed -- see theory section for justification */
  const float soundspeed = hydro_get_comoving_soundspeed(p);

  /* Compute the Balsara switch */
  const float balsara =
      abs_div_v / (abs_div_v + curl_v + 0.0001f * soundspeed * fac_B / p->h);

  /* Compute the "grad h" term */
  const float common_factor = p->h / (hydro_dimension * p->density.wcount);
  const float grad_h_term = (p->density.pressure_bar_dh * common_factor *
                             hydro_one_over_gamma_minus_one) /
                            (1.f + common_factor * p->density.wcount_dh);

  /* Update variables. */
  p->force.f = grad_h_term;
  p->force.soundspeed = soundspeed;
  p->force.balsara = balsara;
}

/**
 * @brief Resets the variables that are required for a gradient calculation.
 *
 * This function is called after hydro_prepare_gradient.
 *
 * @param p The particle to act upon.
 * @param xp The extended particle data to act upon.
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static void hydro_reset_gradient(
    struct part *restrict p) {

  p->viscosity.v_sig = 2.f * p->force.soundspeed;
}

/**
 * @brief Finishes the gradient calculation.
 *
 * Just a wrapper around hydro_gradients_finalize, which can be an empty method,
 * in which case no gradients are used.
 *
 * This method also initializes the force loop variables.
 *
 * @param p The particle to act upon.
 */
__attribute__((always_inline)) INLINE static void hydro_end_gradient(
    struct part *p) {

  /* Some smoothing length multiples. */
  const float h = p->h;
  const float h_inv = 1.0f / h;                       /* 1/h */
  const float h_inv_dim = pow_dimension(h_inv);       /* 1/h^d */
  const float h_inv_dim_plus_one = h_inv_dim * h_inv; /* 1/h^(d+1) */

  /* Include the extra factors in the del^2 u */

  p->diffusion.laplace_u *= 2.f * h_inv_dim_plus_one;
}

/**
 * @brief Sets all particle fields to sensible values when the #part has 0 ngbs.
 *
 * In the desperate case where a particle has no neighbours (likely because
 * of the h_max ceiling), set the particle fields to something sensible to avoid
 * NaNs in the next calculations.
 *
 * @param p The particle to act upon
 * @param xp The extended particle data to act upon
 * @param cosmo The cosmological model.
 */
__attribute__((always_inline)) INLINE static void hydro_part_has_no_neighbours(
    struct part *restrict p, struct xpart *restrict xp,
    const struct cosmology *cosmo) {

  /* Some smoothing length multiples. */
  const float h = p->h;
  const float h_inv = 1.0f / h;                 /* 1/h */
  const float h_inv_dim = pow_dimension(h_inv); /* 1/h^d */

  /* Re-set problematic values */
  p->rho = p->mass * kernel_root * h_inv_dim;
  p->viscosity.v_sig = 0.f;
  p->pressure_bar =
      p->mass * p->u * hydro_gamma_minus_one * kernel_root * h_inv_dim;
  p->density.wcount = kernel_root * h_inv_dim;
  p->density.rho_dh = 0.f;
  p->density.wcount_dh = 0.f;
  p->density.pressure_bar_dh = 0.f;

  p->density.rot_v[0] = 0.f;
  p->density.rot_v[1] = 0.f;
  p->density.rot_v[2] = 0.f;

  /* Probably not shocking, so this is safe to do */
  p->viscosity.div_v = 0.f;
  p->diffusion.laplace_u = 0.f;
}

/**
 * @brief Prepare a particle for the force calculation.
 *
 * This function is called in the ghost task to convert some quantities coming
 * from the density loop over neighbours into quantities ready to be used in the
 * force loop over neighbours. Quantities are typically read from the density
 * sub-structure and written to the force sub-structure.
 * Examples of calculations done here include the calculation of viscosity term
 * constants, thermal conduction terms, hydro conversions, etc.
 *
 * @param p The particle to act upon
 * @param xp The extended particle data to act upon
 * @param cosmo The current cosmological model.
 * @param hydro_props Hydrodynamic properties.
 * @param dt_alpha The time-step used to evolve non-cosmological quantities such
 *                 as the artificial viscosity.
 */
__attribute__((always_inline)) INLINE static void hydro_prepare_force(
    struct part *restrict p, struct xpart *restrict xp,
    const struct cosmology *cosmo, const struct hydro_props *hydro_props,
    const float dt_alpha) {

  /* Here we need to update the artificial viscosity */

  /* We use in this function that h is the radius of support */
  const float kernel_support_physical = p->h * cosmo->a * kernel_gamma;
  const float kernel_support_physical_inv = 1.f / kernel_support_physical;
  const float v_sig_physical = p->viscosity.v_sig * cosmo->a_factor_sound_speed;
  const float soundspeed_physical = hydro_get_physical_soundspeed(p, cosmo);

  const float sound_crossing_time_inverse =
      soundspeed_physical * kernel_support_physical_inv;

  /* Construct time differential of div.v implicitly following the ANARCHY spec
   */

  const float div_v_dt =
      dt_alpha == 0.f
          ? 0.f
          : (p->viscosity.div_v - p->viscosity.div_v_previous_step) / dt_alpha;

  /* Construct the source term for the AV; if shock detected this is _positive_
   * as div_v_dt should be _negative_ before the shock hits */
  const float S = kernel_support_physical * kernel_support_physical *
                  max(0.f, -1.f * div_v_dt);
  /* 0.25 factor comes from our definition of v_sig (sum of soundspeeds rather
   * than mean). */
  /* Note this is v_sig_physical squared, not comoving */
  const float v_sig_square = 0.25 * v_sig_physical * v_sig_physical;

  /* Calculate the current appropriate value of the AV based on the above */
  const float alpha_loc =
      hydro_props->viscosity.alpha_max * S / (v_sig_square + S);

  if (alpha_loc > p->viscosity.alpha) {
    /* Reset the value of alpha to the appropriate value */
    p->viscosity.alpha = alpha_loc;
  } else {
    /* Integrate the alpha forward in time to decay back to alpha = alpha_loc */
    p->viscosity.alpha =
        alpha_loc + (p->viscosity.alpha - alpha_loc) *
                        expf(-dt_alpha * sound_crossing_time_inverse *
                             hydro_props->viscosity.length);
  }

  /* Check that we did not hit the minimum */
  p->viscosity.alpha =
      max(p->viscosity.alpha, hydro_props->viscosity.alpha_min);

  /* Set our old div_v to the one for the next loop */
  p->viscosity.div_v_previous_step = p->viscosity.div_v;

  /* Now for the diffusive alpha */

  const float diffusion_timescale_physical_inverse =
      v_sig_physical * kernel_support_physical_inv;

  const float sqrt_u_inv = 1.f / sqrtf(p->u);

  /* Calculate initial value of alpha dt before bounding */
  /* Evolution term: following Schaller+ 2015. This is made up of several
     cosmology factors: physical smoothing length, sound speed from laplace(u) /
     sqrt(u), and the 1 / a^2 coming from the laplace operator. */
  float alpha_diff_dt = hydro_props->diffusion.beta * kernel_support_physical *
                        p->diffusion.laplace_u * cosmo->a_factor_sound_speed *
                        sqrt_u_inv * cosmo->a2_inv;

  /* Decay term: not documented in Schaller+ 2015 but was present
   * in the original EAGLE code and in appendix of Schaye+ 2015 */
  alpha_diff_dt -= (p->diffusion.alpha - hydro_props->diffusion.alpha_min) *
                   diffusion_timescale_physical_inverse;

  float new_diffusion_alpha = p->diffusion.alpha;
  new_diffusion_alpha += alpha_diff_dt * dt_alpha;

  /* Consistency checks to ensure min < alpha < max */
  new_diffusion_alpha =
      min(new_diffusion_alpha, hydro_props->diffusion.alpha_max);
  new_diffusion_alpha =
      max(new_diffusion_alpha, hydro_props->diffusion.alpha_min);

  p->diffusion.alpha = new_diffusion_alpha;
}

/**
 * @brief Reset acceleration fields of a particle
 *
 * Resets all hydro acceleration and time derivative fields in preparation
 * for the sums taking  place in the various force tasks.
 *
 * @param p The particle to act upon
 */
__attribute__((always_inline)) INLINE static void hydro_reset_acceleration(
    struct part *restrict p) {

  /* Reset the acceleration. */
  p->a_hydro[0] = 0.0f;
  p->a_hydro[1] = 0.0f;
  p->a_hydro[2] = 0.0f;

  /* Reset the time derivatives. */
  p->u_dt = 0.0f;
  p->force.h_dt = 0.0f;
}

/**
 * @brief Sets the values to be predicted in the drifts to their values at a
 * kick time
 *
 * @param p The particle.
 * @param xp The extended data of this particle.
 */
__attribute__((always_inline)) INLINE static void hydro_reset_predicted_values(
    struct part *restrict p, const struct xpart *restrict xp) {

  /* Re-set the predicted velocities */
  p->v[0] = xp->v_full[0];
  p->v[1] = xp->v_full[1];
  p->v[2] = xp->v_full[2];

  /* Re-set the entropy */
  p->u = xp->u_full;

  /* Compute the sound speed */
  const float soundspeed = hydro_get_comoving_soundspeed(p);

  p->force.soundspeed = soundspeed;
}

/**
 * @brief Predict additional particle fields forward in time when drifting
 *
 * Additional hydrodynamic quantites are drifted forward in time here. These
 * include thermal quantities (thermal energy or total energy or entropy, ...).
 *
 * Note the different time-step sizes used for the different quantities as they
 * include cosmological factors.
 *
 * @param p The particle.
 * @param xp The extended data of the particle.
 * @param dt_drift The drift time-step for positions.
 * @param dt_therm The drift time-step for thermal quantities.
 * @param cosmo The cosmological model.
 * @param hydro_props The properties of the hydro scheme.
 * @param floor_props The properties of the entropy floor.
 */
__attribute__((always_inline)) INLINE static void hydro_predict_extra(
    struct part *restrict p, const struct xpart *restrict xp, float dt_drift,
    float dt_therm, const struct cosmology *cosmo,
    const struct hydro_props *hydro_props,
    const struct entropy_floor_properties *floor_props) {

  /* Predict the internal energy */
  p->u += p->u_dt * dt_therm;

  /* Check against entropy floor */
  const float floor_A = entropy_floor(p, cosmo, floor_props);
  const float floor_u = gas_internal_energy_from_entropy(p->rho, floor_A);

  /* Check against absolute minimum */
  const float min_u =
      hydro_props->minimal_internal_energy / cosmo->a_factor_internal_energy;

  p->u = max(p->u, floor_u);
  p->u = max(p->u, min_u);

  const float h_inv = 1.f / p->h;

  /* Predict smoothing length */
  const float w1 = p->force.h_dt * h_inv * dt_drift;
  if (fabsf(w1) < 0.2f)
    p->h *= approx_expf(w1); /* 4th order expansion of exp(w) */
  else
    p->h *= expf(w1);

  /* Predict density and weighted pressure */
  const float w2 = -hydro_dimension * w1;
  if (fabsf(w2) < 0.2f) {
    const float expf_approx =
        approx_expf(w2); /* 4th order expansion of exp(w) */
    p->rho *= expf_approx;
    p->pressure_bar *= expf_approx;
  } else {
    const float expf_exact = expf(w2);
    p->rho *= expf_exact;
    p->pressure_bar *= expf_exact;
  }

  /* Compute the new sound speed */
  const float soundspeed = hydro_get_comoving_soundspeed(p);

  p->force.soundspeed = soundspeed;
}

/**
 * @brief Finishes the force calculation.
 *
 * Multiplies the force and accelerations by the appropiate constants
 * and add the self-contribution term. In most cases, there is little
 * to do here.
 *
 * Cosmological terms are also added/multiplied here.
 *
 * @param p The particle to act upon
 * @param cosmo The current cosmological model.
 */
__attribute__((always_inline)) INLINE static void hydro_end_force(
    struct part *restrict p, const struct cosmology *cosmo) {

  p->force.h_dt *= p->h * hydro_dimension_inv;
}

/**
 * @brief Kick the additional variables
 *
 * Additional hydrodynamic quantites are kicked forward in time here. These
 * include thermal quantities (thermal energy or total energy or entropy, ...).
 *
 * @param p The particle to act upon.
 * @param xp The particle extended data to act upon.
 * @param dt_therm The time-step for this kick (for thermodynamic quantities).
 * @param dt_grav The time-step for this kick (for gravity quantities).
 * @param dt_hydro The time-step for this kick (for hydro quantities).
 * @param dt_kick_corr The time-step for this kick (for gravity corrections).
 * @param cosmo The cosmological model.
 * @param hydro_props The constants used in the scheme
 * @param floor_props The properties of the entropy floor.
 */
__attribute__((always_inline)) INLINE static void hydro_kick_extra(
    struct part *restrict p, struct xpart *restrict xp, float dt_therm,
    float dt_grav, float dt_hydro, float dt_kick_corr,
    const struct cosmology *cosmo, const struct hydro_props *hydro_props,
    const struct entropy_floor_properties *floor_props) {

  /* Integrate the internal energy forward in time */
  const float delta_u = p->u_dt * dt_therm;

  /* Do not decrease the energy by more than a factor of 2*/
  xp->u_full = max(xp->u_full + delta_u, 0.5f * xp->u_full);

  /* Check against entropy floor */
  const float floor_A = entropy_floor(p, cosmo, floor_props);
  const float floor_u = gas_internal_energy_from_entropy(p->rho, floor_A);

  /* Check against absolute minimum */
  const float min_u =
      hydro_props->minimal_internal_energy / cosmo->a_factor_internal_energy;

  /* Take highest of both limits */
  const float energy_min = max(min_u, floor_u);

  if (xp->u_full < energy_min) {
    xp->u_full = energy_min;
    p->u_dt = 0.f;
  }
}

/**
 * @brief Converts hydro quantity of a particle at the start of a run
 *
 * This function is called once at the end of the engine_init_particle()
 * routine (at the start of a calculation) after the densities of
 * particles have been computed.
 * This can be used to convert internal energy into entropy for instance.
 *
 * @param p The particle to act upon
 * @param xp The extended particle to act upon
 * @param cosmo The cosmological model.
 * @param hydro_props The constants used in the scheme.
 */
__attribute__((always_inline)) INLINE static void hydro_convert_quantities(
    struct part *restrict p, struct xpart *restrict xp,
    const struct cosmology *cosmo, const struct hydro_props *hydro_props) {

  /* Convert the physcial internal energy to the comoving one. */
  /* u' = a^(3(g-1)) u */
  const float factor = 1.f / cosmo->a_factor_internal_energy;
  p->u *= factor;
  xp->u_full = p->u;

  /* Apply the minimal energy limit */
  const float min_energy =
      hydro_props->minimal_internal_energy / cosmo->a_factor_internal_energy;
  if (xp->u_full < min_energy) {
    xp->u_full = min_energy;
    p->u = min_energy;
    p->u_dt = 0.f;
  }

  /* Note that unlike Minimal the pressure and sound speed cannot be calculated
   * here because they are smoothed properties in this scheme. */

  /* Set the initial value of the artificial viscosity based on the non-variable
     schemes for safety */

  p->viscosity.alpha = hydro_props->viscosity.alpha;
  /* Initialise this here to keep all the AV variables together */
  p->viscosity.div_v_previous_step = 0.f;

  /* Set the initial values for the thermal diffusion */
  p->diffusion.alpha = hydro_props->diffusion.alpha;
}

/**
 * @brief Initialises the particles for the first time
 *
 * This function is called only once just after the ICs have been
 * read in to do some conversions or assignments between the particle
 * and extended particle fields.
 *
 * @param p The particle to act upon
 * @param xp The extended particle data to act upon
 */
__attribute__((always_inline)) INLINE static void hydro_first_init_part(
    struct part *restrict p, struct xpart *restrict xp) {

  p->time_bin = 0;
  p->wakeup = time_bin_not_awake;
  xp->v_full[0] = p->v[0];
  xp->v_full[1] = p->v[1];
  xp->v_full[2] = p->v[2];
  xp->a_grav[0] = 0.f;
  xp->a_grav[1] = 0.f;
  xp->a_grav[2] = 0.f;
  xp->u_full = p->u;

  hydro_reset_acceleration(p);
  hydro_init_part(p, NULL);
}

/**
 * @brief Overwrite the initial internal energy of a particle.
 *
 * Note that in the cases where the thermodynamic variable is not
 * internal energy but gets converted later, we must overwrite that
 * field. The conversion to the actual variable happens later after
 * the initial fake time-step.
 *
 * @param p The #part to write to.
 * @param u_init The new initial internal energy.
 */
__attribute__((always_inline)) INLINE static void
hydro_set_init_internal_energy(struct part *p, float u_init) {

  p->u = u_init;
}

#endif /* SWIFT_ANARCHY_PU_HYDRO_H */
