Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations
SIAM Journal on Scientific and Statistical Computing
Three-dimensional adaptive mesh refinement for hyperbolic conservation laws
SIAM Journal on Scientific Computing
Good neighborhoods for multidimensional Van Leer limiting
Journal of Computational Physics
SIAM Journal on Optimization
Second-order sign-preserving conservative interpolation (remapping) on general grids
Journal of Computational Physics
An efficient linearity-and-bound-preserving remapping method
Journal of Computational Physics
A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods
Journal of Computational Physics
The repair paradigm: New algorithms and applications to compressible flow
Journal of Computational Physics
Analysis and computation of a least-squares method for consistent mesh tying
Journal of Computational and Applied Mathematics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Linearity-preserving flux correction and convergence acceleration for constrained Galerkin schemes
Journal of Computational and Applied Mathematics
A flux-corrected transport algorithm for handling the close-packing limit in dense suspensions
Journal of Computational and Applied Mathematics
Optimization---Based modeling with applications to transport: part 1. abstract formulation
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Optimization-Based modeling with applications to transport: part 2. the optimization algorithm
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Optimization-Based modeling with applications to transport: part 3. computational studies
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Journal of Computational Physics
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We develop and study the high-order conservative and monotone optimization-based remap (OBR) of a scalar conserved quantity (mass) between two close meshes with the same connectivity. The key idea is to phrase remap as a global inequality-constrained optimization problem for mass fluxes between neighboring cells. The objective is to minimize the discrepancy between these fluxes and the given high-order target mass fluxes, subject to constraints that enforce physically motivated bounds on the associated primitive variable (density). In so doing, we separate accuracy considerations, handled by the objective functional, from the enforcement of physical bounds, handled by the constraints. The resulting OBR formulation is applicable to general, unstructured, heterogeneous grids. Under some weak requirements on grid proximity, but not on the cell types, we prove that the OBR algorithm is linearity preserving in one, two and three dimensions. The paper also examines connections between the OBR and the recently proposed flux-corrected remap (FCR), Liska et al. [1]. We show that the FCR solution coincides with the solution of a modified version of OBR (M-OBR), which has the same objective but a simpler set of box constraints derived by using a ''worst-case'' scenario. Because M-OBR (FCR) has a smaller feasible set, preservation of linearity may be lost and accuracy may suffer for some grid configurations. Our numerical studies confirm this, and show that OBR delivers significant increases in robustness and accuracy. Preliminary efficiency studies of OBR reveal that it is only a factor of 2.1 slower than FCR, but admits 1.5 times larger time steps.