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

The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form. This paper specifically focuses on Euler system that is used for modeling…

A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…

In this work, we suggest an easy-to-code higher-order finite volume semi-discrete scheme to analyze the nonlinear behavior of the electron-plasma oscillations by solving electron fluid equations numerically. The present method employs a…

Radiative heat transfer is a fundamental process in high energy density physics and inertial fusion. Accurately predicting the behavior of Marshak waves across a wide range of material properties and drive conditions is crucial for design…

We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is…

In this paper, we develop a simple, efficient, and fifth-order finite difference interpolation-based Hermite WENO (HWENO-I) scheme for one- and two-dimensional hyperbolic conservation laws. We directly interpolate the solution and…

We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlocal diffusion operators in the basis of spherical harmonics,…

In this article we present the first better than second order accurate unstructured Lagrangian-type one-step WENO finite volume scheme for the solution of hyperbolic partial differential equations with non-conservative products. The method…

As computational astrophysics comes under pressure to become a precision science, there is an increasing need to move to high accuracy schemes for computational astrophysics. Hence the need for a specialized review on higher order schemes…

In this paper, we introduce a superconvergent approximation method that employs radial basis functions (RBFs) in the numerical solution of conservation laws. The use of RBFs for interpolation and approximation is a well developed area of…

High order reconstruction in the finite volume (FV) approach is achieved by a more fundamental form of the fifth order WENO reconstruction in the framework of orthogonally-curvilinear coordinates, for solving the hyperbolic conservation…

In this paper, we develop parametrized positivity satisfying flux limiters for the high order finite difference Runge-Kutta weighted essentially non-oscillatory (WENO) scheme solving compressible Euler equations to maintain positive density…

We propose a simple yet effective local smoothness indicator for the downwind stencil in central-upwind weighted essentially non-oscillatory (WENO) schemes of even order for hyperbolic conservation laws. Starting from an odd-order upwind…

Shallow water surface flows commonly entrain sediments, resulting in scouring and/or deposition of the underlying substrate that may strongly influence the pattern of subsequent flow. These coupled phenomena, which can be investigated…

An efficient algorithm for calculating radiative transfer on massively parallel computers using domain decomposition is presented. The integral formulation of the transfer equation is used to divide the problem into a local but…

In this paper, a new five-point targeted essentially non-oscillatory (TENO) scheme with adaptive dissipation is proposed. With the standard TENO weighting strategy, the cut-off parameter $C_T$ determines the nonlinear numerical dissipation…

One of the fundamental challenges in image restoration is denoising, where the objective is to estimate the clean image from its noisy measurements. To tackle such an ill-posed inverse problem, the existing denoising approaches generally…

We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of…

Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation. In this paper we transfer this into frequency domain, where…

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 this scheme is derived from our previous work [J. Comput.…