High resolution finite volume computations on unstructured grids using solution dependent weighted least squares gradients

An improved high resolution finite volume method based on linear and quadratic variable reconstructions using solution dependent weighted least squares (SDWLS) gradients has been presented here. An extended stencil consisting of vertex-based neighbours of a cell is used in the higher order reconstructions for inviscid flux computations. A QR algorithm with Householder transformation is used to solve the weighted least squares problem. In case of Navier–Stokes equations, viscous fluxes are discretized in a central differencing manner based on the Coirier’s diamond path. A few inviscid and viscous test cases are solved in order to demonstrate the efficacy of the present method. Progressive improvements in solution accuracy are observed with the increase in the order of variable reconstructions. In most cases, results of quadratic reconstruction show significant improvements over that of linear reconstruction.