Journal of Computational Physics
Incremental remapping as a transport&slash;advection algorithm
Journal of Computational Physics
Toward an oscillation-free, mass conservative, Eulerian-Lagrangian transport model
Journal of Computational Physics
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 high-order finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM)
Journal of Computational Physics
Adaptive moment-of-fluid method
Journal of Computational Physics
ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method
Journal of Computational Physics
Failsafe flux limiting and constrained data projections for equations of gas dynamics
Journal of Computational Physics
Hi-index | 31.47 |
Repair is a conservative, post-processing procedure to be used in numerical methods for hyperbolic conservation laws in order to preserve certain qualitative characteristics of the numerical solution, such as positivity of density and internal energy, by means of redistribution of conserved quantities such as mass, momentum and total energy among the cells of the mesh. In this paper we describe the repair paradigm and prove several theorems which form a theoretical foundation for the repair procedures. We consider two applications of repair and present corresponding numerical results. The first application deals with improving properties of the remapping (conservative interpolation) stage of arbitrary Lagrangian-Eulerian (ALE) methods for the gas dynamics equations, in which the solution is conservatively transferred from one mesh to another. One requirement for remapping is that the interpolated density and internal energy on the new mesh have to stay positive. Another desirable property is that the remapping procedure should not create new extrema for the velocity field. For various reasons these properties may not be satisfied, especially for high-order methods. Repair plays a supplemental role by bringing gas dynamics quantities into physically justified bounds. Another application of repair is to improve the quality of numerical methods for advection of some scalar tracer field with prescribed divergence-free velocity field, in which case the advection equation can be written as a conservation law, and therefore the total amount of tracer is conserved. We show how the repair procedure allows us to reduce oscillations in a numerical solution obtained by a formally high-order method. Repair offers an alternative to more classical methods of reducing oscillations and maintaining positivity.