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The MUSCL scheme is a one-parameter family of schemes, where the choice of the parameter gives different schemes; Van Leer originally developed it. For instance if you choose kappa, the parameter to be 0.5, then you get the QUICK scheme. Whatever you choose the formula has been derived for a structured grid. It assumes equal spacing between grid points, and requires local co-linearity of points, i.e. they must be in a straight line. This can only be achieved with an orthogonal structured grid. There are some papers that for instance introduce a curvature factor, to take account of non co-linearity, and other papers that introduce a stretching factor, to take account of non local grid spacing but essentially they are there to adapt something that is designed for structured grids to be made usable on unstructured grids. <BR><BR>Since Barth of NASA introduce linear reconstruction and reconstruction in general (1989 ish) MUSCL has not used in proper academic codes on unstructured grids. These have no requirement of grid spacing and do not require a local co-linearity of points; importantly they reduce the dependence of the convective differencing on grid spacing and quality. The most important point is that in a MUSCL framework a multi-dimensional limiter cannot be used and only simple min-mod limiters can be used, which clips the primitive variables non-physically and are not differentiable. Using a multi-dimensional limiter with linear reconstruction allows the gradients to be limited physically, thereby allowing a more correct solution and a limiter that is differentiable. <BR><BR>The problem is that most people doing cold flow do not realize this, and it is in fact excellently highlighted in combustion LES. I would recommend switching if you have the chance and time. |
发表于 2005-9-7 23:00
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发表于 2005-9-8 15:51
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