Optimization-Based modeling with applications to transport: part 3. computational studies

Authors:
Denis Ridzal;Joseph Young;Pavel Bochev;Kara Peterson
Affiliations:
Optimization and Uncertainty Quantification, Sandia National Laboratories, Albuquerque, NM;Numerical Analysis and Applications, Sandia National Laboratories, Albuquerque, NM;Numerical Analysis and Applications, Sandia National Laboratories, Albuquerque, NM;Numerical Analysis and Applications, Sandia National Laboratories, Albuquerque, NM
Venue:
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Year:
2011

Citing 7
Cited 3

High-resolution conservative algorithms for advection in incompressible flow

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Incremental remapping as a transport&slash;advection algorithm

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Second-order sign-preserving conservative interpolation (remapping) on general grids

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Optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian-Eulerian methods

Journal of Computational Physics
Formulation, analysis and numerical study of an optimization-based conservative interpolation (remap) of scalar fields for arbitrary Lagrangian-Eulerian methods

Journal of Computational Physics
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 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 remap and transport: A divide and conquer strategy for feature-preserving discretizations

Journal of Computational Physics

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Abstract

This paper is the final of three related articles that develop and demonstrate a new optimization-based framework for computational modeling. The framework uses optimization and control ideas to assemble and decompose multiphysics operators and to preserve their fundamental physical properties in the discretization process. One application of the framework is in the formulation of robust algorithms for optimization-based transport (OBT). Based on the theoretical foundations established in Part 1 and the optimization algorithm for the solution of the remap subproblem, derived in Part 2, this paper focuses on the application of OBT to a set of benchmark transport problems. Numerical comparisons with two other transport schemes based on incremental remapping, featuring flux-corrected remap and the linear reconstruction with van Leer limiting, respectively, demonstrate that OBT is a competitive transport algorithm.