Title: Synchronized Flux-Corrected Remapping of Mass and Momentum for ALE Methods Speaker: M. Shashkov, Group T-5, Los Alamos National Laboratory, Los Alamos, USA Date/Time: Monday June 29, 2009, 10:00am - 11:00am Location: CSRI Building, Room 90 (Sandia NM) Brief Abstract: We propose a FCT-based algorithm for conservative, local bounds preserving interpolations to be used for synchronized remapping of mass and momentum in ALE computations. For the case of cell-centered conserved quantities and continuous rezone strategy, the remapping part of an ALE computation can be formulated with in terms of inter-cell fluxes [1] and viewed as a global optimization problem. Since direct solution of such problem is not practical, we show how it can be replaced by a series of local optimization problems, using the ideas of Flux-Corrected Transport (FCT). The original FCT method [2] combines low-order fluxes, which by definition preserve local bounds (e.g. in density and velocity), with more accurate higher-order fluxes, which might violate the bounds if used alone. Many modifications have been suggested, including improvement of flux-correctors, straightforward extension to multiple dimensions and introduction of iterations to increase accuracy [3, 4]. A good review can be found in [5]. To our best knowledge, few attempts have been done to extend the method nontrivially for coupled systems of equations. Most of the current implementations treat each equation separately by a scalar method and adjust the correction factors a posteriori, which might lead to over- restriction of fluxes and physically problematic results. Treatment of more equations at once by imposing a priori constraints has been pioneered in [4], which inspired our work and is used for comparison. On each cell interface, our Synchronized Flux-Corrected Remapping (SFCR) method constructs a complete set of constraints imposed by local bounds for density and velocity to find a suitable set of correction factors for inter-cell fluxes of mass and momentum. By doing this we avoid performing the global optimization, but still obtain fluxes that are more accurate than the low-order fluxes while preserving the local bounds. Moreover, from the physical point of view, this process does not violate the causality principle. While the method is independent on dimension and mesh topology, its features and performance will be demonstrated in 1D and on structured quadrilateral mesh in 2D. References: CSRI POC: John Shadid, (505) 845-7876 |