High-Order Unstructured Spectral Finite Volume Scheme for Aerodynamic Applications

Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows

“…Nevertheless, the comparison here considers a second-order WENO scheme and a third-order SFV scheme. If such a comparison had considered third-order schemes in both cases, previous experience [16] indicates that the SFV method would easily outperform the WENO calculation even in terms of wall-clock time.…”

“…It should be pointed out that the same numerical test case was studied in [16], considering only the linear boundary representation. It was observed in that effort that the low-order boundary treatment causes a shock wave to develop close to the inner boundary, which then makes the limiter active.…”

“…This flux computation can be carried out using a flux vector splitting procedure or an exact or approximate Riemann solver. The latter procedure is adopted in the present work and the numerical flux can be written as f qx rq ; y rq n r f Riemann q L x rq ; y rq ; q R x rq ; y rq ; n r (16) where q L is the conserved variable vector obtained by the p i polynomial applied at the x rq ; y rq coordinates and q R is the same vector obtained with the p nb polynomial in the same coordinates of the edge. Note that the nb subscript represents the element to the right of the edge, whereas the i subscript denotes the CV to its left.…”

“…Moreover, the polynomial base functions for the linear, quadratic and cubic reconstructions are listed in Table 1. For more details regarding partition quality and stability analysis the interested reader is referred to [16,20].…”

“…The use of limiters is necessary when the flow solution contains discontinuities, in order to remove spurious oscillations that may eventually lead to divergence of the numerical solution. Previous work on limiter implementations for high-order methods [16] was based on problem-dependent parameters to determine which elements need limiting and which can limit too many or too few elements of the solution. In the first case, the order of the method is seriously reduced, and in the second case, divergence can occur.…”