Compute HLLC on moving grids in the frame of the face, fix its Jacobians

- Moving grids: the wave speeds, the pressure work of the moving face in the supersonic branches and the term
  V_g (p* - p)/(s - S_M) of the star-state energy were missing or inconsistent, so HLLC was not Galilean
  invariant (NACA0012 M 0.8, fixed grid vs still air and a translating grid: CL -12 %). The flux is now
  computed in the frame of the face (u' = u - w n, H' = H - w u_n + w^2/2) and transformed back
  (F = B F', J = B J' T).
- Jacobians: sign of the velocity term of the general-gas dp/drho. The star-state Jacobians keep by default the
  density of the other state in dp*/dU (inexact, #2198), which was more robust with inexact linear solves in our
  tests; USE_ACCURATE_FLUX_JACOBIANS= YES now gives the exact derivative for fixed wave speeds.
- Unit test hllc_jacobian_tests.cpp: finite differences in 2D and 3D, fixed and moving faces, both sides of
  the contact, all branches, default and exact.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LEL91DW5WPbPwgFtCvHga6

Author: rois1995

Common/src/CConfig.cpp

@@ -2171,7 +2171,7 @@ void CConfig::SetConfig_Options() {
   addDoubleArrayOption("JST_SENSOR_COEFF", 2, false, jst_coeff);
   /*!\brief LAX_SENSOR_COEFF \n DESCRIPTION: 1st order artificial dissipation coefficients for the Lax-Friedrichs method. \ingroup Config*/
   addDoubleOption("LAX_SENSOR_COEFF", Kappa_1st_Flow, 0.15);
-  /*!\brief USE_ACCURATE_FLUX_JACOBIANS \n DESCRIPTION: Use numerically computed Jacobians for AUSM+up(2) and SLAU(2) \ingroup Config*/
+  /*!\brief USE_ACCURATE_FLUX_JACOBIANS \n DESCRIPTION: Use numerically computed Jacobians for AUSM+up(2) and SLAU(2), exact Jacobians (for fixed wave speeds) for HLLC \ingroup Config*/
   addBoolOption("USE_ACCURATE_FLUX_JACOBIANS", Use_Accurate_Jacobians, false);
   /*!\brief CENTRAL_JACOBIAN_FIX_FACTOR \n DESCRIPTION: Improve the numerical properties (diagonal dominance) of the global Jacobian matrix, 3 to 4 is "optimum" (central schemes) \ingroup Config*/
   addDoubleOption("CENTRAL_JACOBIAN_FIX_FACTOR", Cent_Jac_Fix_Factor, 4.0);

SU2_CFD/include/numerics/flow/convection/hllc.hpp

@@ -39,6 +39,7 @@
 class CUpwHLLC_Flow final : public CNumerics {
 private:
   bool implicit, dynamic_grid;
+  bool useAccurateJacobian; /*!< \brief Jacobians computed exactly for fixed wave speeds (USE_ACCURATE_FLUX_JACOBIANS). */
   unsigned short iDim, jDim, iVar, jVar;
 
   su2double *IntermediateState;
@@ -55,6 +56,8 @@ class CUpwHLLC_Flow final : public CNumerics {
   su2double *dSm_dU, *dPI_dU, *drhoStar_dU, *dpStar_dU, *dEStar_dU;
 
   su2double* Flux;        /*!< \brief The flux accross the face. */
+  bool fixedWaveSpeeds = false;     /*!< \brief Use fixed_sL, fixed_sR as wave speeds (verification of the Jacobians). */
+  su2double fixed_sL = 0.0, fixed_sR = 0.0;
   su2double** Jacobian_i; /*!< \brief The Jacobian w.r.t. point i after computation. */
   su2double** Jacobian_j; /*!< \brief The Jacobian w.r.t. point j after computation. */
 
@@ -79,6 +82,18 @@ class CUpwHLLC_Flow final : public CNumerics {
    */
   ResidualType<> ComputeResidual(const CConfig* config) override;
 
+  /*!
+   * \brief Fix the left and right wave speeds (relative to the face), for the verification of the Jacobians, which
+   *        treat them as constants.
+   * \param[in] active - Use the fixed values.
+   * \param[in] val_sL, val_sR - Left and right wave speeds.
+   */
+  inline void SetFixedWaveSpeeds(bool active, su2double val_sL, su2double val_sR) {
+    fixedWaveSpeeds = active;
+    fixed_sL = val_sL;
+    fixed_sR = val_sR;
+  }
+
 };
 
 /*!
@@ -91,6 +106,7 @@ class CUpwHLLC_Flow final : public CNumerics {
 class CUpwGeneralHLLC_Flow final : public CNumerics {
 private:
   bool implicit, dynamic_grid;
+  bool useAccurateJacobian; /*!< \brief Jacobians computed exactly for fixed wave speeds (USE_ACCURATE_FLUX_JACOBIANS). */
   unsigned short iDim, jDim, iVar, jVar;
 
   su2double *IntermediateState;
@@ -108,6 +124,8 @@ class CUpwGeneralHLLC_Flow final : public CNumerics {
   su2double *dSm_dU, *dPI_dU, *drhoStar_dU, *dpStar_dU, *dEStar_dU;
 
   su2double* Flux;        /*!< \brief The flux accross the face. */
+  bool fixedWaveSpeeds = false;     /*!< \brief Use fixed_sL, fixed_sR as wave speeds (verification of the Jacobians). */
+  su2double fixed_sL = 0.0, fixed_sR = 0.0;
   su2double** Jacobian_i; /*!< \brief The Jacobian w.r.t. point i after computation. */
   su2double** Jacobian_j; /*!< \brief The Jacobian w.r.t. point j after computation. */
 
@@ -132,6 +150,18 @@ class CUpwGeneralHLLC_Flow final : public CNumerics {
    */
   ResidualType<> ComputeResidual(const CConfig* config) override;
 
+  /*!
+   * \brief Fix the left and right wave speeds (relative to the face), for the verification of the Jacobians, which
+   *        treat them as constants.
+   * \param[in] active - Use the fixed values.
+   * \param[in] val_sL, val_sR - Left and right wave speeds.
+   */
+  inline void SetFixedWaveSpeeds(bool active, su2double val_sL, su2double val_sR) {
+    fixedWaveSpeeds = active;
+    fixed_sL = val_sL;
+    fixed_sR = val_sR;
+  }
+
   /*!
    * \brief Compute the Average quantities for a general fluid flux between two nodes i and j.
    * Using the approach of Vinokur and Montagne'