An unstructured grid implementation of high-order spectral finite volume schemes

Abstract

The present work implements the spectral finite volume scheme in a cell centered finite volume context for unstructured meshes. The 2-D Euler equations are considered to represent the flows of interest. The spatial discretization scheme is developed to achieve high resolution and computational efficiency for flow problems governed by hyperbolic conservation laws, including flow discontinuities. Such discontinuities are mainly shock waves in the aerodynamic studies of interest in the present paper. The entire reconstruction process is described in detail for the 2 nd to 4 th order schemes. Roe's flux difference splitting method is used as the numerical Riemann solver. Several applications are performed in order to assess the method capability compared to data available in the literature. The results obtained with the present method are also compared to those of essentially nonoscillatory and weighted essentially non-oscillatory high-order schemes. There is a good agreement with the comparison data and efficiency improvements have been observed.

Numerical simulation of 1-D oil and water displacements in petroleum reservoirs using the spectral finite volume method

“…27is used to deal with discontinuity in the numerical solution. It is important to note that, when the limiter function is employed to avoid numerical oscillations in non-smooth regions, the piecewise reconstructed high-order polynomial on SVs is noncontinuous, then an approximated Riemann solver must be applied [7,40]. Eq.…”

Automated adaptive TFSF method for solving time domain Maxwell's equations

“…The spectral finite volume (SFV) method of Wang et al 10,11 is used in discretizing the spatial integral terms for higher order spatial accuracy. In the SFV method, the computational domain is divided into finite number (N) of nonoverlapping triangles called spectral volume (SV).…”

Unsteady Aerodynamic Applications Using High-Order Unstructured Grid Methods

“…Furthermore, in unsteady applications in which such very fine meshes have to be moved in order to accommodate the airfoil motion, previous experience 7 has demonstrated that one ends up with a very stiff aerodynamic solver and, hence, extremely expensive unsteady computations. Therefore, the interest in extending the previously available high-order capability 3,8 in order to treat unsteady flows with moving and/or deforming grids. Although the present work will only consider inviscid flows, the main idea is that the use of high-order methods could lessen the needs for mesh refinement at the solid walls and, hence, reduce computational costs and many of the problems which have been observed in Ref.…”