A High-Resolution Procedure for Euler and Navier–Stokes Computations on Unstructured Grids

A finite-volume procedure, comprising a gradient-reconstruction technique and a multidimensional limiter, has been proposed for upwind algorithms on unstructured grids. The high-resolution strategy, with its inherent dependence on a wide computational stencil, does not suffer from a catastrophic loss of accuracy on a grid with poor connectivity as reported recently with many unstructured-grid limiting procedures. The continuously differentiable limiter is shown to be effective for strong discontinuities, even on a grid which is composed of highly distorted triangles, without adversely affecting convergence to steady state. Numerical experiments involving transient computations of two-dimensional scalar convection to steady-state solutions of Euler and Navier–Stokes equations demonstrate the capabilities of the new procedure.