Showing papers on "MUSCL scheme published in 1991"
TL;DR: In this article, a flux limiter based on characteristic variables is extended by a control volume flux formulation to approximate the convection term at the cell interface for an essentially third-order-accurate scheme.
Abstract: A flux limiter based on characteristic variables is extended by a control volume flux formulation to approximate the convection term at the cell interface for an essentially third-order-accurate scheme. The basic algorithm uses implicit MUSCL-type flux splitting and the approximate factorization method. It is applied to three test problems: (i) a one-dimensional shock tube problem; (ii) a two-dimensional problem of an oblique shock step with Mach numbers 3 and 10 and a shock angle of 59°;(iii) a two-dimensional problem of transonic inviscid flow past an NACA0012 aerofoil with Mach number 0·8 at zero angle of attack. The computational results by the new flux limiter function are compared with the results of direct applications of the SMART algorithm, Leonard's SHARP algorithm, the third-order Van Leer flux-splitting method with a smooth limiter, Harten's second-order unwind-biased TVD scheme, Chakravarthy's third-order MUSCL-type TVD scheme and the exact solution. The comparison shows that the present method gives the most accurate and least oscillatory results with a rapid rate of convergence.
31 citations
01 Jan 1991
TL;DR: In this paper, the performance of variants of the Full Approximation Multigrid Scheme in the computation of complex recirculating flows, both laminar and turbulent, was investigated.
Abstract: The paper reports a study on the performance of variants of the Full Approximation Multigrid Scheme in the computation of complex recirculating flows, both laminar and turbulent. The MG variants are implemented into a three-dimensional, non-orthogonal, collocated finite-volume procedure in which the Cartesian velocity components and the pressure are determined via a pressure-correction algorithm. Convection is approximated by three methods: a first-order hybrid scheme combining the central and upwind approximations, the quadratic upstream-weighted QUICK scheme and the TVD-type MUSCL scheme. Three turbulence models are considered: a low-Re and a high-Re variant of the two-equation k-e eddy-viscosity model, and a Reynolds-stress-transport closure, all implemented within a non-orthogonal grid environment. Multigrid performance is investigated for four cases: a laminar flow in a 2D plane constriction, a laminar flow in a 3D skewed lid-driven cavity, a turbulent flow in a constricted pipe, computed with two eddy-viscosity models, and a turbulent flow behind a 2D backward-facing step, computed with a Reynolds-stress-transport model within a strongly distorted non-orthogonal mesh. Convergence acceleration is shown to be significant in turbulent conditions but not of the same order as that for laminar flows.
22 citations