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.
This content will become publicly available on September 1, 2025
- Award ID(s):
- 2208438
- PAR ID:
- 10535734
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Communications on Applied Mathematics and Computation
- Volume:
- 6
- Issue:
- 3
- ISSN:
- 2096-6385
- Page Range / eLocation ID:
- 2011 to 2044
- Subject(s) / Keyword(s):
- Hyperbolic conservation and balance laws with uncertainties · Finite-volume methods · Central-upwind schemes · Weighted essentially non-oscillatory (WENO) interpolations
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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