Numerical solution of a first‐order conservation equation by a least square method

Publisher Website
Google Scholar
Abstract
Least square methods have been frequently used to solve fluid mechanics problems. Their specific usefulness is emphasized for the solution of a first‐order conservation equation. On the one hand, the least square formulation embeds the first‐order problem into equivalent second‐order problem, better adapted to discretization techniques due to symmetry and positive‐definiteness of the associated matrix. On the other hand, the introduction of a least square functional is convenient for finite element applications.This approach is applied to the model problem of the conservation of mass (the unknown is the density ρ) in a nozzle with a specified velocity field (u, v), possibly including jumps along lines simulating shock waves. This represent a preliminary study towards the solution of the steady Euler equations.A finite difference and a finite element method are presented. The choice of the finite difference scheme and of a continuous finite element representation for the groups of variables (ρu, ρv) is discussed in terms of conservation of mass flux. Results obtained with both methods are compared in two numerical tests with the same mesh system.

This publication has 3 references indexed in Scilit: