Journal of Computational Physics
Nonet-Cartesian Grid Method for Shock Flow Computations
Journal of Scientific Computing
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
Journal of Computational Physics
Second-order Godunov-type scheme for reactive flow calculations on moving meshes
Journal of Computational Physics
On Resistive MHD Models with Adaptive Moving Meshes
Journal of Scientific Computing
Adaptive unstructured volume remeshing - I: The method
Journal of Computational Physics
Central schemes on overlapping cells
Journal of Computational Physics
Space---Time Adaptive Solution of First Order PDES
Journal of Scientific Computing
A Bi-Hyperbolic Finite Volume Method on Quadrilateral Meshes
Journal of Scientific Computing
Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws
Journal of Scientific Computing
A simple moving mesh method for one-and two-dimensional phase-field equations
Journal of Computational and Applied Mathematics - Special issue: International conference on mathematics and its application
Journal of Computational Physics
Resolving small-scale structures in Boussinesq convection by adaptive grid methods
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
An adaptive grid method for two-dimensional viscous flows
Journal of Computational Physics
An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
Journal of Computational Physics
A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation
Journal of Computational Physics
An efficient adaptive mesh redistribution method for a non-linear Dirac equation
Journal of Computational Physics
Level Set Calculations for Incompressible Two-Phase Flows on a Dynamically Adaptive Grid
Journal of Scientific Computing
Resolving the shock-induced combustion by an adaptive mesh redistribution method
Journal of Computational Physics
An adaptive mesh redistribution method for the incompressible mixture flows using phase-field model
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An adaptive ghost fluid finite volume method for compressible gas-water simulations
Journal of Computational Physics
Remapping-free ALE-type kinetic method for flow computations
Journal of Computational Physics
Adaptive Runge-Kutta discontinuous Galerkin methods using different indicators: One-dimensional case
Journal of Computational Physics
An adaptive GRP scheme for compressible fluid flows
Journal of Computational Physics
A simple moving mesh method for one- and two-dimensional phase-field equations
Journal of Computational and Applied Mathematics
A self-adaptive moving mesh method for the Camassa-Holm equation
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Dimension-splitting data points redistribution for meshless approximation
Journal of Computational and Applied Mathematics
A high-resolution mapped grid algorithm for compressible multiphase flow problems
Journal of Computational Physics
Automatic grid control in adaptive BVP solvers
Numerical Algorithms
Comparison of some Lie-symmetry-based integrators
Journal of Computational Physics
Simulating finger phenomena in porous media with a moving finite element method
Journal of Computational Physics
A Second-Order Accurate Conservative Front-Tracking Method in One Dimension
SIAM Journal on Scientific Computing
A direct Eulerian GRP scheme for relativistic hydrodynamics: One-dimensional case
Journal of Computational Physics
A numerical study of air-vapor-heat transport through textile materials with a moving interface
Journal of Computational and Applied Mathematics
A direct Eulerian GRP scheme for relativistic hydrodynamics: Two-dimensional case
Journal of Computational Physics
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
The adaptive GRP scheme for compressible fluid flows over unstructured meshes
Journal of Computational Physics
Adaptive numerical simulation of traffic flow density
Computers & Mathematics with Applications
Journal of Scientific Computing
A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
Journal of Computational Physics
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We develop efficient moving mesh algorithms for one- and two-dimensional hyperbolic systems of conservation laws. The algorithms are formed by two independent parts: PDE evolution and mesh-redistribution. The first part can be any appropriate high-resolution scheme, and the second part is based on an iterative procedure. In each iteration, meshes are first redistributed by an equidistribution principle, and then on the resulting new grids the underlying numerical solutions are updated by a conservative-interpolation formula proposed in this work. The iteration for the mesh-redistribution at a given time step is complete when the meshes governed by a nonlinear equation reach the equilibrium state. The main idea of the proposed method is to keep the mass-conservation of the underlying numerical solution at each redistribution step. In one dimension, we can show that the underlying numerical approximation obtained in the mesh-redistribution part satisfies the desired TVD property, which guarantees that the numerical solution at any time level is TVD, provided that the PDE solver in the first part satisfies such a property. Several test problems in one and two dimensions are computed using the proposed moving mesh algorithm. The computations demonstrate that our methods are efficient for solving problems with shock discontinuities, obtaining the same resolution with a much smaller number of grid points than the uniform mesh approach.