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Mimetic Metrics for the DGSEM.

Daniel Bach1, Andrés Rueda-Ramírez2, David A Kopriva3

  • 1University of Cologne, Cologne, Germany.

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Summary
This summary is machine-generated.

Researchers developed a new method for computing metric terms in numerical solvers. This ensures divergence-free metric terms, crucial for preserving free-stream properties and ensuring entropy stability on curvilinear grids.

Keywords:
Curved MeshesDiscontinuous GalerkinDivergence Free MethodsFree-Stream PreservationMimetic Methods

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Scientific computing

Background:

  • Free-stream preservation is vital for accurate numerical simulations on curvilinear grids.
  • Existing methods struggle to maintain this property due to challenges with metric terms.
  • Divergence-free metric terms are essential for both free-stream preservation and entropy stability.

Purpose of the Study:

  • To introduce a novel approach for calculating metric terms in discontinuous Galerkin spectral element methods (DGSEMs).
  • To ensure that these computed metric terms are divergence-free.
  • To enhance the stability and accuracy of numerical solvers on complex geometries.

Main Methods:

  • A mimetic approach is employed for computing metric terms.
  • The method utilizes projections compatible with de Rham Cohomology.
  • This ensures discrete metric identities are satisfied, leading to divergence-free terms.

Main Results:

  • The proposed method guarantees divergence-free metric terms for DGSEMs.
  • This directly addresses the key requirement for free-stream preservation.
  • The approach contributes to improved entropy stability on curvilinear grids.

Conclusions:

  • The new mimetic approach provides a robust way to compute divergence-free metric terms.
  • This significantly advances the capabilities of numerical solvers on curvilinear grids.
  • The method offers a pathway to more accurate and stable computational simulations.