The convection-diffusion equation is a fundamental that exists widely. consists of two processes: diffusion and convection. can also be called drift-diffusion equaintion. convection – mainly characterizes natural phenomenon in which physical particles, energy are transferred system. well-known linear transport one kind equation. describe the scalar field such as material feature, chemical react...

The monotonicity and stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability and monotonicity of a non-linear scheme in terms of its corresponding scheme in variations. Such an approach leads to application of the stability theory for linear equation systems to establish stability ...

Since the Industrial Revolution, humanity has been intensifying burning of fossil fuels and as a consequence, average temperature on Earth increasing. The 20th century was warmest future prospects are not favorable, that is, even higher temperatures expected. This demonstrates importance studies subject, mainly to predict possible environmental, social economic consequences. objective this work...

By revisiting the basic Godunov approach for linear system of hyperbolic Partial Differential Equations (PDEs) we show that it is hybridizable. As such, it is a natural recipe for us to constructively and systematically establish a unified HDG framework for a large class of PDEs including those of Friedrichs’ type. The unification is fourfold. First, it provides a single constructive procedure ...

Article history: Received 5 March 2012 Received in revised form 28 September 2012 Accepted 1 October 2012 Available online 23 October 2012

A robust second order, shock-capturing numerical scheme for multi-dimensional special relativistic magnetohydrodynamics on computational domains with adaptive mesh refinement is presented. The base solver is a total variation diminishing Lax-Friedrichs scheme in a finite volume setting and is combined with a diffusive approach for controlling magnetic monopole errors. The consistency between th...

This paper is to study the decay rate for perturbations of stationary discrete shocks for the Lax-Friedrichs scheme approximating the scalar conservation laws by means of an elementary weighted energy method. If the summation of the initial perturbation over (−∞, j) is small and decays at the algebraic rate as |j| → ∞, then the solution approaches the stationary discrete shock profiles at the c...

A discontinuous Galerkin shallow water model on the cubed sphere is developed, thereby extending the transport scheme developed by Nair et al. The continuous flux form nonlinear shallow water equations in curvilinear coordinates are employed. The spatial discretization employs a modal basis set consisting of Legendre polynomials. Fluxes along the element boundaries (internal interfaces) are app...

We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to high dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta tim...