SIAM Journal on Numerical Analysis
The three R's of engineering analysis and error estimation and adaptivity
Computer Methods in Applied Mechanics and Engineering
An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
Journal of Computational Physics
A projection method for locally refined grids
Journal of Computational Physics
An Adaptive Mesh Projection Method for Viscous Incompressible Flow
SIAM Journal on Scientific Computing
Adaptive mesh refinement and multilevel iteration for flow in porous media
Journal of Computational Physics
Journal of Computational Physics
Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
SIAM Journal on Numerical Analysis
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
Designing an efficient solution stragety for fluid flows
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
An approach to local refinement of structured grids
Journal of Computational Physics
Nested Cartesian grid method in incompressible viscous fluid flow
Journal of Computational Physics
Adaptive meshless centres and RBF stencils for Poisson equation
Journal of Computational Physics
A solution-adaptive lattice Boltzmann method for two-dimensional incompressible viscous flows
Journal of Computational Physics
Hi-index | 31.47 |
In this paper, a solution-adaptive algorithm is presented for the simulation of incompressible viscous flows. The framework of this method consists of an adaptive local stencil refinement algorithm and 3-points central difference discretization. The adaptive local stencil refinement is designed in such a manner that 5-points symmetric stencil is guaranteed at each interior node, so that conventional finite difference formula can be easily constructed everywhere in the domain. Thus, high efficiency and accuracy of central difference scheme can be ultimately enjoyed together with the solution-adaptive property. The adaptive finite difference method has been tested by three numerical examples, to examine its performance in the two-dimensional problems. The numerical examples include Poisson equation, moving interface problem and a lid-driven incompressible flow problem. It was found that the multigrid approach can be efficiently combined with solution-adaptive algorithm to speed up the convergence rate.