Monotonic, multidimensional flux discretization scheme for all Peclet numbers

The focus of this work is to resolve discontinuities in the flow by a hybrid scheme comprising two classes of flux discretization schemes. Construction of a stiffness matrix having the M-matrix property is desirable 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 equation are proposed and compared. The first class of finite-element method is suited for high-Peclet-number problems and is formulated within the Galerkin context. The other class of upwind scheme, which is applicable to lower-Peclet-number flows, falls into the Petrov-Galerkin category. The finite-element test and basis spaces are spanned by Legendre polynomials. Assessment studies are made, with emphasis on the accuracy and stability of the solution. We also address the sensitivity of this scheme to Peclet numbers in obtaining monotonic solutions. Numerical investigation reveals that the pro...

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