Multidimensional upwinding method

P. Colella, Multidimensional Upwind Methods for Hyperbolic Conservation Laws, LBL-17023, Lawrence Berkley Laboratory, Berkley, CA, 1984. 

The newer method of Bortels et al., called multidimensional upwinding method (MDUM) should also be mentioned [127]. It was applied to a problem involving diffusion, convection and migration, both steady state and timemarching. 

In addition to the topics reviewed above, which form the vast majority of the articles published to date in the field of electrochemical simulation, there are a number of other alternative methods that have been exploited by workers. These include, statistical techniques such as the Monte Carlo method [174-179], which has been exploited to examine the fractal nature of electrode surfaces and electrodeposited polymer film growth. The finite volume method, which has found significant application in the engineering literature [180, 181], remains poorly exploited in the electrochemical field [182, 183] as does the multidimensional upwinding method, which has been applied by Van Den Boss-che and coworkers [184, 185] to multi-ion systems at the rotating disc electrode. For recent advances, readers are referred to the review of Speiser [19]. 

Hughes, T. J.R. and Brooks, A.N., 1979, A multidimensional upwind scheme with no cross-wind diffusion. In Hughes, I . J. R. (ed.), Finite Element Methods for Convection Dominated Flows, AMD Vol. 34, ASME, New York. 

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