Multi-Resolution Analysis for ENO Schemes
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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Given a function ux which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which ux can be recovered to a prescribed accuracy. We apply this multi resolution analysis to ENO schemes in order to reduce the number of numerical flux computations which is needed in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. We present an efficient algorithm for implementing this program in the one dimensional case this algorithm can be extended to the multi-dimensional case with cartesian grids.
- Numerical Mathematics
- Fluid Mechanics