Meshfree method for the navier-stokes equations

Abstract

Numerical solutions of fluid dynamics problems by meshfree method are considered. Among various versions of meshfree method, the moving least squre reproducing kernel method or briefly speaking MLSRK method is employed for the space approximation. Objective governing equations for fluid problems include stationary incompressible Stokes and Navier-Stokes equations, non-stationary incompressible Stokes and Navier-Stokes equations, and non-stationary compressible Euler equations. For each governing equations, the existence of approximated solution and convergence analysis are considered. Each chapter is concluded with numerical examples using meshfree method. for the convergence analysis, basic projection error analysis is systematically studied. Theoretical study for stationary conservation law is contained in the last chapter. Main results include existence of solutions under critical integrability conditions.