Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A wavelet optimized adaptive multi-domain method
Journal of Computational Physics
A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method
SIAM Journal on Scientific Computing
Spectral Simulation of Supersonic Reactive Flows
SIAM Journal on Numerical Analysis
High Order Schemes for Resolving Waves: Number of Points per Wavelength
Journal of Scientific Computing
High-order/spectral methods of unstructured grids I. Time-domain solution of Maxwell''s equations
High-order/spectral methods of unstructured grids I. Time-domain solution of Maxwell''s equations
High Order Schemes for Resolving Waves: Number of Points per Wavelength
Journal of Scientific Computing
Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping
Journal of Scientific Computing
An adaptive multiresolution scheme with local time stepping for evolutionary PDEs
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
Journal of Computational Physics
Hi-index | 0.02 |
Adaptive Mesh Refinement (AMR) schemes are generally considered promising because of the ability of the scheme to place grid points or computational degrees of freedom at the location in the flow where truncation errors are unacceptably large. For a given order, AMR schemes can reduce work. However, for the computation of turbulent or non-turbulent mixing when compared to high order non-adaptive methods, traditional 2nd order AMR schemes are computationally more expensive. We give precise estimates of work and restrictions on the size of the small scale grid and show that the requirements on the AMR scheme to be cheaper than a high order scheme are unrealistic for most computational scenarios.