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The design of the NewFilter interface loosely follow the Non-Virtual Interface pattern
DoExecutePartition are supposed to be overridden by subclasses and be private. The only occasion for them to be
protected is when a subclass is further extended and the sub-subclasses needs to call the subclass'
In this particular case, making
private also ensure that subclass'
DoExecutePartition will not accidentally call
NewFilterParticleAdvection::DoExecute without overriding it first, which will result in infinite recursion (since