Third order residual distribution schemes for the Navier-Stokes equations
We construct a third order multidimensional upwind residual distribution scheme for the system of the Navier-Stokes equations. The underlying approximation is obtained using standard P(2) Lagrange finite elements. To discretise the inviscid component of the equations, each element is divided in sub-elements over which we compute a high order residual defined as the integral of the inviscid fluxes on the boundary of the sub-element. The residuals are distributed to the nodes of each sub-element in a multi-dimensional upwind way. To obtain a discretisation of the viscous terms consistent with this multi-dimensional upwind approach, we make use of a Petrov-Galerkin analogy. The analogy allows to find a family of test functions which can be used to obtain a weak approximation of the viscous terms. The performance of this high-order method is tested on flows with high and low Reynolds number. (C) 2010 Elsevier Inc. All rights reserved.
residual distribution schemes viscous term high order schemes