55 citations · 371 across the 31 of their papers we have counts for
31 papers
High order well-balanced and total-energy-conserving local discontinuous Galerkin methods for compressible self-gravitating Euler equations
Liang Pan, Wei Chen, Jianxian Qiu +1
In this paper, we develop a high order structure-preserving local discontinuous Galerkin (DG) scheme for the compressible self-gravitating Euler equations, which pose great challen…
A High-Order Compact Hermite Difference Method for Double-Diffusive Convection
Jianqing Yang, Jianxian Qiu
In this paper, a class of high-order compact finite difference Hermite scheme is presented for the simulation of double-diffusive convection. To maintain linear stability, the conv…
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 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…
A well-balanced moving mesh discontinuous Galerkin method for the Ripa model on triangular meshes
Weizhang Huang, Ruo Li, Jianxian Qiu +1
A well-balanced moving mesh discontinuous Galerkin (DG) method is proposed for the numerical solution of the Ripa model -- a generalization of the shallow water equations that acco…
Moment-based multi-resolution HWENO scheme for hyperbolic conservation laws
Jiayin Li, Chi-Wang Shu, Jianxian Qiu
In this paper, a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory (HWENO) scheme is designed for hyperbolic conservation laws. The main idea of…
A study on CFL conditions for the DG solution of conservation laws on adaptive moving meshes
Min Zhang, Weizhang Huang, Jianxian Qiu
The selection of time step plays a crucial role in improving stability and efficiency in the Discontinuous Galerkin (DG) solution of hyperbolic conservation laws on adaptive moving…
High order finite difference Hermite WENO fixed-point fast sweeping method for static Hamilton-Jacobi equations
Yupeng Ren, Yulong Xing, Jianxian Qiu
In this paper, we combine the nonlinear HWENO reconstruction in \cite{newhwenozq} and the fixed-point iteration with Gauss-Seidel fast sweeping strategy, to solve the static Hamilt…
High order asymptotic preserving Hermite WENO fast sweeping method for the steady-state transport equation
Yupeng Ren, Yulong Xing, Dean Wang +1
In this paper, we propose to combine the fifth order Hermite weighted essentially non-oscillatory (HWENO) scheme and fast sweeping method (FSM) for the solution of the steady-state…
High Order Residual Distribution Conservative Finite Difference HWENO Scheme for Steady State Problems
Jianfang Lin, Yupeng Ren, Rémi Abgrall +1
In this paper, we develop a high order residual distribution (RD) method for solving steady state conservation laws in a novel Hermite weighted essentially non-oscillatory (HWENO)…
A quasi-conservative DG-ALE method for multi-component flows using the non-oscillatory kinetic flux
Dongmi Luo, Shiyi Li, Weizhang Huang +2
A high-order quasi-conservative discontinuous Galerkin (DG) method is proposed for the numerical simulation of compressible multi-component flows. A distinct feature of the method…
High order finite difference Hermite WENO fast sweeping methods for static Hamilton-Jacobi equations
Yupeng Ren, Yulong Xing, Jianxian Qiu
In this paper, we propose a novel Hermite weighted essentially non-oscillatory (HWENO) fast sweeping method to solve the static Hamilton-Jacobi equations efficiently. During the HW…
A hybrid WENO method with modified ghost fluid method for compressible two-medium flow problems
Zhuang Zhao, Yibing Chen, Jianxian Qiu
In this paper, we develop a simplified hybrid weighted essentially non-oscillatory (WENO) method combined with the modified ghost fluid method (MGFM) [28] to simulate the compressi…
A well-balanced positivity-preserving quasi-Lagrange moving mesh DG method for the shallow water equations
Min Zhang, Weizhang Huang, Jianxian Qiu
A high-order, well-balanced, positivity-preserving quasi-Lagrange moving mesh DG method is presented for the shallow water equations with non-flat bottom topography. The well-balan…
A quasi-conservative discontinuous Galerkin method for multi-component flows using the non-oscillatory kinetic flux
Dongmi Luo, Jianxian Qiu, Jun Zhu +1
In this paper, a high order quasi-conservative discontinuous Galerkin (DG) method using the non-oscillatory kinetic flux is proposed for the 5-equation model of compressible multi-…
A high-order well-balanced positivity-preserving moving mesh DG method for the shallow water equations with non-flat bottom topography
Min Zhang, Weizhang Huang, Jianxian Qiu
A rezoning-type adaptive moving mesh discontinuous Galerkin method is proposed for the numerical solution of the shallow water equations with non-flat bottom topography. The well-b…
A Hermite WENO scheme with artificial linear weights for hyperbolic conservation laws
Zhuang Zhao, Jianxian Qiu
In this paper, a fifth-order Hermite weighted essentially non-oscillatory (HWENO) scheme with artificial linear weights is proposed for one and two dimensional hyperbolic conservat…
High-order conservative positivity-preserving DG-interpolation for deforming meshes and application to moving mesh DG simulation of radiative transfer
Min Zhang, Weizhang Huang, Jianxian Qiu
Solution interpolation between deforming meshes is an important component for several applications in scientific computing, including indirect arbitrary-Lagrangian-Eulerian and rez…
A hybrid Hermite WENO scheme for hyperbolic conservation laws
Zhuang Zhao, Yibing Chen, Jianxian Qiu
In this paper, we propose a hybrid finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for solving one and two dimensional hyperbolic conservation laws. The z…
A quasi-Lagrangian moving mesh discontinuous Galerkin method for hyperbolic conservation laws
Dongmi Luo, Weizhang Huang, Jianxian Qiu
A moving mesh discontinuous Galerkin method is presented for the numerical solution of hyperbolic conservation laws. The method is a combination of the discontinuous Galerkin metho…
High order residual distribution for steady state problems for hyperbolic conservation laws}
Jianfang Lin, Rémi Abgrall, Jianxian Qiu
In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentia…
An adaptive moving mesh discontinuous Galerkin method for the radiative transfer equation
Min Zhang, Juan Cheng, Weizhang Huang +1
The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering.…