Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws
Journal of Scientific Computing
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 moving mesh method for two-dimensional ideal magnetohydrodynamics
Journal of Computational Physics
Level Set Calculations for Incompressible Two-Phase Flows on a Dynamically Adaptive Grid
Journal of Scientific Computing
An adaptive mesh redistribution method for the incompressible mixture flows using phase-field model
Journal of Computational Physics
An adaptive ghost fluid finite volume method for compressible gas-water simulations
Journal of Computational Physics
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
An adaptive GRP scheme for compressible fluid flows
Journal of Computational Physics
Numerical analysis and implementational aspects of a new multilevel grid deformation method
Applied Numerical Mathematics
The adaptive GRP scheme for compressible fluid flows over unstructured meshes
Journal of Computational Physics
Metric tensors for the interpolation error and its gradient in Lp norm
Journal of Computational Physics
On numerical modeling of animal swimming and flight
Computational Mechanics
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This work presents the first effort in designing a moving mesh algorithm to solve the incompressible Navier--Stokes equations in the primitive variables formulation. The main difficulty in developing this moving mesh scheme is how to keep it divergence-free for the velocity field at each time level. The proposed numerical scheme extends a recent moving grid method based on harmonic mapping [R. Li, T. Tang, and P. W. Zhang, J. Comput. Phys., 170 (2001), pp. 562--588], which decouples the PDE solver and the mesh-moving algorithm. This approach requires interpolating the solution on the newly generated mesh. Designing a divergence-free-preserving interpolation algorithm is the first goal of this work. Selecting suitable monitor functions is important and is found challenging for the incompressible flow simulations, which is the second goal of this study. The performance of the moving mesh scheme is tested on the standard periodic double shear layer problem. No spurious vorticity patterns appear when even fairly coarse grids are used.