MONOTONIC, MULTIDIMENSIONAL FLUX DISCRETIZATION SCHEME FOR ALL PECLETNUMBERS

The focus of this work is to resolve discontinuities in the flow by a hybrid scheme comprising two classes of flux discretization schemes. C onstruction of a stiffness matrix having the M-matrix property is desi rable in finite-element codes for capturing a solution profile with an appreciable gradient. in this study, two finite-element formulations capable of yielding an irreducible diagonal dominant type of matrix eq uation are proposed and compared. The first class of finite-element me thod is suited for high-Peclet-number problems and is formulated withi n the Galerkin context. The other class of upwind scheme, which is app licable to lower-Peclet-number flows, falls into the Petrov-Galerkin c ategory. The finite-element test and basis spaces are spanned by Legen dre polynomials. Assessment studies are made, with emphasis on the acc uracy and stability of the solution. We also address the sensitivity o f this scheme to Peclet numbers in obtaining monotonic solutions. Nume rical investigation reveals that the proposed scheme is effective in p roducing monotonic solutions at high- and low-Peclet-number conditions .