Moving mesh methods based on moving mesh partial differential equations
Journal of Computational Physics
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
SIAM Journal on Numerical Analysis
Moving Mesh Methods for Problems with Blow-up
SIAM Journal on Scientific Computing
Moving mesh methods with upwinding schemes for time-dependent PDEs
Journal of Computational Physics
Proceedings of international centre for mathematical sciences on Grid adaptation in computational PDES : theory and applications: theory and applications
An efficient dynamically adaptive mesh for potentially singular solutions
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Adaptive Atmospheric Modeling: Key Techniques in Grid Generation, Data Structures, and Numerical Operations with Applications (Lecture Notes in Computational Science and Engineering)
Moving Mesh Generation Using the Parabolic Monge-Ampère Equation
SIAM Journal on Scientific Computing
Modelling atmospheric flows with adaptive moving meshes
Journal of Computational Physics
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We derive a moving mesh method based upon ideas from optimal transport theory which is suited to solving PDE problems in meteorology. In particular we show how the Parabolic Monge-Ampere method for constructing a moving mesh in two-dimensions can be coupled successfully to a pressure correction method for the solution of incompressible flows with significant convection and subject to Coriolis forces. This method can be used to resolve evolving small scale features in the flow. In this paper the method is then applied to the computation of the solution to the Eady problem which is observed to develop large gradients in a finite time. The moving mesh method is shown to work and be stable, and to give significantly better resolution of the evolving singularity than a fixed, uniform mesh.