Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Momentum advection on a staggered mesh
Journal of Computational Physics
Computational methods in Lagrangian and Eulerian hydrocodes
Computer Methods in Applied Mechanics and Engineering
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
An arbitrary Lagrangian-Eulerian computing method for all flow speeds
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Conservative remapping and region overlays by intersecting arbitrary polyhedra
Journal of Computational Physics
Incremental remapping as a transport&slash;advection algorithm
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 subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods
Journal of Computational Physics
A high order ENO conservative Lagrangian type scheme for the compressible Euler equations
Journal of Computational Physics
Journal of Computational Physics
Applied Numerical Mathematics
Positivity-preserving Lagrangian scheme for multi-material compressible flow
Journal of Computational Physics
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An accurate remapping algorithm is an essential component of the Arbitrary Lagrangian-Eulerian (ALE) methods. Most ALE codes applied to high speed flow problems use a staggered mesh, i.e., all the solution variables except the velocities are cell-centered while the velocities are vertex-centered. In this paper, we present a high order accurate conservative remapping method on staggered meshes by using the idea of essentially non-oscillatory (ENO) schemes. The algorithm is based on the ENO reconstruction and approximate integration. On the staggered mesh, two sets of control volumes are built for the cell-centered conserved quantities including the mass and total energy and vertex-centered quantity-momentum respectively. On each rezoning step, we first reconstruct a polynomial function by the cell averages of mass, energy and momentum on their old control volumes. ENO idea is used to choose the best stencils for reconstruction to avoid oscillation. Then, we integrate the reconstructed functions of the old cells over the rezoned cell. These procedures of remapping ensure the algorithm to have the properties of conservation, high order accuracy and essentially non-oscillatory output. A suite of one and two dimensional examples are given to verify the performance of the algorithm.