相关论文: A WENO Algorithm for the Radiative Transfer and Io…

This study presents a high-order finite volume scheme capable of large time-step integration for three-temperature radiation diffusion (3TRD) equations, where conservation is naturally achieved through energy update. To handle local large…

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws are extremely popular because, for multidimensional problems, they offer high order accuracy at a fraction of the cost of finite volume…

This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…

Recently a splitting approach has been presented for the simulation of sonic-boom propagation. Splitting methods allow one to divide complicated partial differential equations into simpler parts that are solved by specifically tailored…

Fixed-point iterative sweeping methods were developed in the literature to efficiently solve steady state solutions of Hamilton-Jacobi equations and hyperbolic conservation laws. Similar as other fast sweeping schemes, the key components of…

We present a quantum field theoretical method for the characterization of disordered complex media with short laser pulses in an optical coherence tomography setup (OCT). We solve this scheme of coherent transport in space and time with…

In this paper, we extend the previous work on absolutely convergent fixed-point fast sweeping WENO methods by Li et al. (J. Comput. Phys. 443: 110516, 2021) and design a fifth-order hybrid fast sweeping scheme for solving steady state…

In this article, novel smoothness indicators are presented for calculating the nonlinear weights of weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi equations. These novel…

In this paper, we propose a new well-balanced fifth-order finite volume WENO method for solving one- and two-dimensional shallow water equations with bottom topography. The well-balanced property is crucial to the ability of a scheme to…

The decisive factor for the calculation accuracy of the mapped weighted essentially non-oscillatory scheme is the width of the center region of the mapping function. Through analysis of the classical mapped WENO schemes, the results show…

In this work, high-order discrete well-balanced methods for one-dimensional hyperbolic systems of balance laws are proposed. We aim to construct a method whose discrete steady states correspond to solutions of arbitrary high-order ODE…

High order fast sweeping methods for efficiently solving steady state solutions of hyperbolic PDEs were not available yet on unstructured meshes. In this paper, we extend high order fast sweeping methods to unstructured triangular meshes by…

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 conservation laws, where the zeroth-order and the first-order moments…

We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation and it is accurate for optically thin, thick, and intermediate…

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady state solutions of hyperbolic partial differential equations (PDEs). As other types of fast sweeping…

We present a new multidimensional classical hydrodynamics code based on Semidiscrete Central Godunov-type schemes and high order Weighted Essentially Non-oscillatory (WENO) data reconstruction. This approach is a lot simpler and easier to…

This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured triangular meshes. We rigorously prove that the proposed method…

A novel procedure is given for choosing smoothest stencil to construct less oscillatory ENO schemes. The procedure is further used to define smoothness parameter in the non-linear weights of new WENO schemes. The main significant features…

We compare the predictions of four different algorithms for the distribution of ionized gas during the Epoch of Reionization. These algorithms are all used to run a 100 Mpc/h simulation of reionization with the same initial conditions. Two…