Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
A conservative fully adaptive multiresolution algorithm for parabolic PDEs
Journal of Computational Physics
An adaptive multiscale finite volume solver for unsteady and steady state flow computations
Journal of Computational Physics
Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping
Journal of Scientific Computing
High order Hybrid central-WENO finite difference scheme for conservation laws
Journal of Computational and Applied Mathematics
Adaptive multiresolution WENO schemes for multi-species kinematic flow models
Journal of Computational Physics
Journal of Computational Physics
A multiresolution finite volume scheme for two-dimensional hyperbolic conservation laws
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media
Journal of Scientific Computing
Variational multiscale element-free Galerkin method for 2D Burgers' equation
Journal of Computational Physics
Applied Numerical Mathematics
An adaptive multiresolution method on dyadic grids: Application to transport equations
Journal of Computational and Applied Mathematics
A one-time truncate and encode multiresolution stochastic framework
Journal of Computational Physics
Journal of Computational Physics
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A generalization of Harten's multiresolution algorithms to two-dimensional (2-D) hyperbolic conservation laws is presented. Given a Cartesian grid and a discretized function on it, the method computes the local-scale components of the function by recursive diadic coarsening of the grid. Since the function's regularity can be described in terms of its scale or multiresolution analysis, the numerical solution of conservation laws becomes more efficient by eliminating flux computations wherever the solution is smooth. Instead, in those locations, the divergence of the solution is interpolated from the next coarser grid level. First, the basic 2-D essentially nonoscillatory (ENO) scheme is presented, then the 2-D multiresolution analysis is developed, and finally the subsequent scheme is tested numerically. The computational results confirm that the efficiency of the numerical scheme can be considerably improved in two dimensions as well.