ISSN:
0271-2091
Keywords:
SUPG finite element method
;
multidimensional upwinding
;
cell vertex advection schemes
;
Euler equations
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Vertex-based multidimensional upwind schemes for scalar advection are compared with shock-capturing SUPG finite element methods based on linear triangular elements. Both methods share the same compact stencil and are formulated as cell-wise residual distribution methods. The distribution for the finite element method is 1/3, supplemented with a Lax-Wendrov-type dissipation term, while the distribution for the upwind schemes is limited to the downstream nodes of the element. The multidimensional upwind schemes use positivity as the monotonicity criterion, while the finite element method includes a residual-based non-linear dissipation.For hyperbolic systems such as the compressible Euler equations the upwind method relies on a multidimensional wave model to decompose the residual into scalar contributions. From this observation a new SUPG formulation for systems is proposed in which the scalar SUPG method is applied to each of the decomposed residuals obtained from the wave model, thereby providing a better-founded definition of the τ dissipation matrix and shock-capturing term in the SUPG methods.
Additional Material:
14 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650200815
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