Draft: Add positivity-preserving entropy-based adaptive filtering for Euler and NS equations

Issue/feature addressed

This merge request introduces the positivity-preserving entropy-based adaptive filtering method for the 1D Euler equation. The method is designed to function both as a shock-capturing mechanism and as a stabilization technique, particularly useful for initialising challenging flow conditions.

Proposed solution

An adaptive filtering method for shock capturing for the compressible flow solver is implemented. This methodology does not require problem-dependent parameter tuning.

Implementation

In this code, an abstract base class called Filtering is implemented, which serves as an interface for different filtering methods. The Filtering class provides a common encapsulation for filtering, allowing derived classes to implement specific filtering techniques. A derived class called PositivityPreservingEntropy is created, which inherits from Filtering and provides a specific filtering implementation. The derived class overrides and implements the pure virtual functions v_Apply defined in Filtering through polymorphism, allowing different filtering techniques to be utilized interchangeably through the base Filtering interface.

In order to be able to apply the filtering technique, two pure virtual functions (methods) are implemented in the UnsteadySystem class. The functions are v_PreIntegrateFiltering and v_PostIntegrateFiltering. The v_PreIntegrateFiltering is implemented since the filtering method needs to obtain the entropy constraint minimum before the time integration. Then after the integration the v_PostIntegrateFiltering is called to filter the solution. Note that the implementation of these methods happen in the CompressibleFlowSymtem class because we need access to the VariableConverter class.

Tests

The test case below were added

1. solvers/CompressibleFlowSolver/Tests/SodShockTube1D_filtering_PPEB.xml

• This test case checks the filtering method for the explicit Euler solver.

Notes

Checklist

• Functions and classes, or changes to them, are documented.
• User guide/documentation is updated.
• Changelog is updated.
• Suitable tests added for new functionality.
• Contributed code is correctly formatted. (See the contributing guidelines).
• License added to any new files.
• No extraneous files have been added (e.g. compiler output or test data files).