Two upwind finite difference schemes are considered for the numerical solution of a class of semilinear convection-diffusion problems with a small perturbation parameter ε and an attractive boundary turning point. We show that for both schemes the maximum nodal error is bounded by a special weighted `1-type norm of the truncation error. These results are used to establish ε-uniform pointwise co...

This paper is devoted to comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is ut þ ðu uÞx 1⁄4 ðuuxxxÞx, which arises in the context of thin film flow. First we employ implicit schemes and treat both convection and diffusion terms implicitly. Then the convection terms are treated with wellknown explicit schemes, namely Godunov,...

Spurious numerical solutions of problems with closed sub-characteristics by upwind difference schemes, in particular problems of recirculating incompressible flow at high Reynolds numbers, are proved to be due to the anisotropy of the artificial viscosity. Numerical examples are presented to show that even very simple problems, including basic problems in fluid dynamics, are not approximated we...

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional conservation equations of mass, momentum, energy and speciescontinuity to obtain the laminar velocity, temperature and concentration fields for simulation of polymerization of styrene in arbitrary cross-sectional duct reactors. Variable physical properties (except for speci...

In this paper, we develop and study numerical methods for the two-mode shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407–432]. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerica...

Residual distribution schemes are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution is globally continuous, defined by a Finite Element space based on triangular Lagrangian Pk elements. A natural subtriangulation of these elements allows the reuse of simple distribution formula previously developed for linear P1 triangles. Th...

In the present work, we are interested in the direct numerical simulation of the compressible Euler and Navier Stokes equations at low Mach number regime. First, we propose a review of existing work on the subject in order to identify the issues raised by the simulation of in this kind of flow, and the existing relevant solutions. Then, we will test different selected compressible low Mach solv...

Numerical modeling of convection suitable for nite volume methods for steady-state, multidimensional, incompressible, turbulent ows is considered. Two methods used to achieve higher order accurate and oscillation-free solutions are discussed, namely ux limiting and variable normalization. A uniied formulation, which brings together most existing higher order monotonicity preserving schemes, is ...