Meshless Local Petrov-Galerkin (MLPG) “Mixed” Approach for Solving Incompressible N-S Equations

Anew Meshless Finite Volume Method through the Meshless Local Petrov-Galerkin (MLPG) (Atluri, 1998) “mixed” approach was developed and successfully used in elasto-static problems by Atluri and Han in 2004, in which a kind of finite volume method was introduced so that the strain and the displacement can be interpolated independently. This “mixed” approach is now extended to steady incompressible fluid flows in the paper. The Navier-Stokes equilibriums are written as the form of MLPG local symmetric weak-form over each sub-domain. Variables of pressure and velocity gradient are interpolated via moving least squares (MLS) or radial basis functions (RBF) independently at the randomly scattered nodes in the local fields as well as velocity, in stead of being expressed by the related velocity in regular MLPG method (Lin, 2001). The order of the continuity of the trial functions can be reduced to C0 instead of C1. Both the lower-order of the continuity and the particular selected Heaviside test function which avoids the integration over domains make the calculation simplified dramatically. Boundary conditions are imposed directly in equilibrium. The 2-D numerical example shows that higher accuracy and computational efficiency are obtained by introducing meshless finite volume method in the “mixed” approach without any other additional skills.