6 papers
Non-splitting Eulerian-Lagrangian WENO schemes for two-dimensional nonlinear convection-diffusion equations
Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu +1
In this paper, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes f…
Provably Convergent and Robust Newton-Raphson Method: A New Dawn in Primitive Variable Recovery for Relativistic MHD
Chaoyi Cai, Jianxian Qiu, Kailiang Wu
A long-standing and formidable challenge faced by all conservative schemes for relativistic magnetohydrodynamics (RMHD) is the recovery of primitive variables from conservative one…
Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics
Chaoyi Cai, Jianxian Qiu, Kailiang Wu
The relativistic hydrodynamics (RHD) equations have three crucial intrinsic physical constraints on the primitive variables: positivity of pressure and density, and subluminal flui…
A compact simple HWENO scheme with ADER time discretization for hyperbolic conservation laws I: structured meshes
Dongmi Luo, Shiyi Li, Jianxian Qiu +2
In this paper, a compact and high order ADER (Arbitrary high order using DERivatives) scheme using the simple HWENO method (ADER-SHWENO) is proposed for hyperbolic conservation law…
Fourth-order conservative non-splitting semi-Lagrangian Hermite WENO schemes for kinetic and fluid simulations
Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu +1
We present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport equations with applications for non…
Simulations of Detonation Wave Propagation in Rectangular Ducts Using a Three-Dimensional WENO Scheme
Hua-Shu Dou, Her Mann Tsai, Boo Cheong Khoo +1
This paper reports high resolution simulations using a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third order TVD Runge-Kutta time stepping method to exa…