A meshfree formulation for the numerical solution of the viscous, compressible Navier-Stokes equations

A meshfree numerical solution procedure consisting of a streamline-upwind Petrov-Galerkin formulation with shock capturing term is presented for the viscous, compressible Navier-Stokes equations in terms of conservation variables. Meshfree methods show similarities to finite elements but result in more general shape functions.; Some concepts of multiresolution analysis and multiple scale analysis are formulated in the context of meshfree methods. Special emphasis is put on orthogonality properties against a set of basis functions. A technique of determining and eliminating hidden zero energy modes in wavelet RKPM and similar methods is developed from the reproducing conditions. The effectiveness of SUPG for meshfree formulations is ascertained by numerical experiments.; With d'Alembert's principle, a method of imposing general boundary and interface conditions for meshfree methods is introduced. Essential boundary conditions are enforced by orthogonalizing against general constraints.; Example computations for viscous, supersonic flows illustrate the viability of the method. The meshfree results compare well to those obtained analytically for changes in flow properties across shock fronts.