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Fourth-Order Conservative Non-splitting Semi-Lagrangian Hermite WENO Schemes for Kinetic and Fluid Simulations.
- Source :
- Journal of Scientific Computing; Jun2024, Vol. 99 Issue 3, p1-34, 34p
- Publication Year :
- 2024
-
Abstract
- We present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport equations with applications for nonlinear problems including the Vlasov–Poisson system, the guiding center Vlasov model, and the incompressible Euler equations in the vorticity-stream function formulation. The proposed SL HWENO schemes combine a weak formulation of the characteristic Galerkin method with two newly constructed HWENO reconstruction methods. The new HWENO reconstructions are meticulously designed to strike a delicate balance between curbing numerical oscillation and introducing excessive dissipation. Mass conservation naturally holds due to the weak formulation of the semi-Lagrangian discontinuous Galerkin method and the design of the HWENO reconstructions. We apply a positivity-preserving limiter to maintain the positivity of numerical solutions when needed. Abundant benchmark tests are performed to verify the effectiveness of the proposed SL HWENO schemes. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08857474
- Volume :
- 99
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Journal of Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 176963286
- Full Text :
- https://doi.org/10.1007/s10915-024-02520-6