Finite volume HWENO schemes for nonconvex conservation laws
Xiaofeng Cai, Jianxian Qiu, Jing-Mei Qiu
TL;DR
This paper investigates the limitations of high order finite volume HWENO schemes for nonconvex conservation laws and proposes modified schemes based on monotone and entropic projections to improve convergence and accuracy.
Contribution
It introduces modified finite volume HWENO schemes using monotone and entropic projections for better performance on nonconvex conservation laws.
Findings
Modified schemes improve convergence to entropy solutions.
Numerical tests demonstrate enhanced accuracy and stability.
Extensions to systems and 2D laws show versatility.
Abstract
We illustrate that numerical solutions of high order finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for some nonconvex conservation laws perform poorly or converge to the entropy solution in a slow speed. The modified finite volume HWENO schemes based either on first order monotone schemes or a second order entropic projection following the work of Qiu and Shu [SIAM J. Sci. Comput., 31 (2008), 584-607] are proposed and compared for solving one-dimensional scalar problems. We extend the modified finite volume HWENO based on first order monotone schemes for one-dimensional systems and two-dimensional scalar conservation laws. Numerical tests for several representative examples will be reported.
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Taxonomy
TopicsComputational Fluid Dynamics and Aerodynamics · Fluid Dynamics and Turbulent Flows · Navier-Stokes equation solutions