Tensor-product adaptive grids based on coordinate transformations
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Nonet-Cartesian Grid Method for Shock Flow Computations
Journal of Scientific Computing
Adaptive moving mesh computations for reaction--diffusion systems
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
Moving mesh methods with locally varying time steps
Journal of Computational Physics
On Resistive MHD Models with Adaptive Moving Meshes
Journal of Scientific Computing
Space---Time Adaptive Solution of First Order PDES
Journal of Scientific Computing
Moving meshes by the deformation method
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
Journal of Computational Physics
Fictitious boundary and moving mesh methods for the numerical simulation of rigid particulate flows
Journal of Computational Physics
An efficient adaptive mesh redistribution method for a non-linear Dirac equation
Journal of Computational Physics
Journal of Computational Physics
Adaptive grid generation based onthe least-squares finite-element method
Computers & Mathematics with Applications
Numerical analysis and implementational aspects of a new multilevel grid deformation method
Applied Numerical Mathematics
SIAM Journal on Scientific Computing
Journal of Computational Physics
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An adaptive remeshing procedure based on a cell volume deformation method is presented. Starting with an initial grid, this method offers direct cell volume control through the specification of the transformation Jacobian. Grid points are moved with appropriate grid velocities so that the specified cell volume distribution can be achieved at the end of the grid movement without adding or removing grid points. The grid velocities are determined by solving a scalar Poisson equation. This method is applied to solving the compressible Euler equations. Computational test cases of transonic flow over an airfoil are presented and demonstrate the desired control of grid sizes across shock waves.