Comparison of three second‐order accurate reconstruction schemes for 2D Euler and Navier–Stokes compressible flows on unstructured grids

Abstract

SUMMARYThis paper reports an intercomparison of three second-order accurate reconstruction schemes to predict 2D steady-state compressible Euler and Navier-Stokes ows on unstructured meshes. The schemes comprise one monotone slope limiter (Barth and Jespersen, A1AA Paper 89-0366, 1989) and two approximately monotone methods: the slope limiter due to Venkatakrishnan and a data-dependent weighting least-squares procedure (Gooch, Journal of Computational Physics, 1997; 133:6 -17). In addition to the 1D scalar wave problem, comparisons were performed under two inviscid test cases: a supersonic 10• ramp and a supersonic bump; and two viscous laminar compressible ow cases: the Blasius boundary layer and a double-throated nozzle. The data-dependent oscillatory behaviour is found to be dependent on a user-supplied constant. The three schemes are compared in terms of accuracy and computational e ciency. The results show that the data-dependent procedure always returns a numerical steady-state solution, more accurate than the ones returned by the slope limiters. Its use for Navier-Stokes ow calculations is recommended.

Newton-Krylov iterative matrix representative spectrum

“…7 (odd iterations only). The shape invariance that can be observed in this figure for all of the coefficient matrices has been numerically observed in all the cases that have been studied [21], not just on the one herein presented. The shape invariance is a research topic that, from this vivid graphical depiction, seems to be worth further investigation regarding a mean to exploit it.…”

“…Regarding accuracy and robusteness, see [10] for an example on the importance of working with nondimensional variables when dealing with shocks. Also consider that the condition number of A is a measure of the sensibility with which the solution is obtained in finite-precision for a corresponding linear system [14].…”

“…The convective terms' spatial discretization proceeds in separate reconstruction and evolution steps. For the reconstruction step, a modified ENO-like data-dependent least-squares procedure is used to obtain a second-order error term [10]. For the evolution step, an approximate Riemann solver is employed [11].…”

Advanced Numerical Solver for Dam-Break Flow Application

“…The robustness of MUSCL-type (monotonic upwind schemes for conservative laws) scheme is demonstrated by Marques and Pereira [15], which MUSCL-type schemes show a closer result with the exact solution of the fluid flow profiles compare to other schemes, like WAF (weighted averaged flux) scheme. Unlike the constant approximation of L U % and R U % by original Godunov scheme, in MUSCLscheme, both L U % and R U % are changing in a linear approximation according to their adjacent cells.…”

Comparison of matrix‐free acceleration techniques in compressible Navier–Stokes calculations

“…This implies separate reconstruction and evolution steps. For the reconstruction step, a data-dependent least-squares procedure is used to obtain a secondorder error term [18]. For the evolution step, the HLLC approximate Riemann solver [19] is employed.…”