We develop a numerical solver for radiative transfer problems based on the weighted essentially nonoscillatory (WENO) scheme modified with anti-diffusive flux corrections, in order to solve the temperature and ionization profiles around a point source of photons in the reionization epoch. Algorithms for such simulation must be able to handle the following two features: 1. the sharp profiles of ...

For reaction–diffusion–advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction–diffusion systems with both stiff reaction and diffusi...

We propose a high order positivity-preserving conservative remapping method on three-dimensional (3D) tetrahedral meshes , based the weighted essentially non-oscillatory (WENO) reconstruction method. By precisely computing overlaps between before and after rezoning step in arbitrary Lagrangian–Eulerian (ALE) framework, our does not limit range of mesh movements has wider applications. This also...

A fluid mixture model of tissue deformations has been studied in this paper. The model is a mixed system of nonlinear hyperbolic and elliptic partial differential equations. Both theoretical linear stability and numerical analysis are presented. Comparisons between standard numerical methods that utilize Runge-Kutta methods coupled with the WENO scheme and the immersed interface methods are giv...

In this paper we incorporate a low magnetic Reynolds number MHD model to a high order CFD algorithm with WENO and a low diffusion scheme for 3D Navier-Stokes equations. We present results for hypersonic laminar flows around a flat plate and around a blunt body, with different strengths of magnetic fields, to demonstrate the methodology. More simulations, including turbulence, are in progress an...

Polymerization of proteins is a biochemical process involved in different diseases. Mathematically, it is generally modeled by aggregation-fragmentation-type equations. In this paper we consider a general polymerization model and propose a high-order numerical scheme to investigate the behavior of the solution. An important property of the equation is the mass conservation. The fifth-order WENO...

This paper is concerned with the development of high order methods for the numerical approximation of one-dimensional nonconservative hyperbolic systems. In particular, we are interested in high order extensions of the generalized Roe methods introduced by I. Toumi in 1992, based on WENO reconstruction of states. We also investigate the well-balanced properties of the resulting schemes. Finally...

Abstract Finite volume, weighted essentially non-oscillatory (WENO) schemes require the computation of a smoothness indicator. This can be expensive, especially in multiple space dimensions. We consider use simple indicator $$\sigma ^{\textrm{S}}= \frac{1}{N_{\textrm{S}}-1}\sum _{j} ({\bar{u}}_{j} - {\bar{u}}_{m})^2$$ <mml:msu...