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Fix ESDIRK scheme for compressible flow solver

Jacques Xing requested to merge CFD-Xing/nektar:fix-esdirk-cfs into master

Issue/feature addressed

Currently, ESDIRK schemes are not working with the implicit Euler solver. This MR solve this problem.

Proposed solution

Here is a description of the implementation:

  • First, as v_DoDiffusion is not implemented for the implicit compressible flow solver, the implicit version of DoOdeRhs must be used.
  • Second, a DoProjection operation is necessary during the initialization of the time-stepping method to ensure proper application of the boundary condition for the implicit compressible flow solver.

Implementation

Tests

The solvers/CompressibleFlowSolver/Tests/IsentropicVortex16Implicit_P8.xml test has been updated to use ESDIRK4_ES6 scheme.

Additional tests have been performed to check the order of convergence of the scheme

DIRKOrder3_ES5:
3.5672647626073934
3.620318792233117
3.411412463774804
DIRKOrder4_ES6:
3.7531758850067445
3.947312510386293
3.99487978001635

Suggested reviewers

Please suggest any people who would be appropriate to review your code.

Notes

Please add any other information that could be useful for reviewers.

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).
Edited by Jacques Xing

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