Adaptive grid refinement for numerical weather prediction
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
An Algorithm for Computing Fekete Points in the Triangle
SIAM Journal on Numerical Analysis
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
Adaptive Atmospheric Modeling: Key Techniques in Grid Generation, Data Structures, and Numerical Operations with Applications (Lecture Notes in Computational Science and Engineering)
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Journal of Computational Physics
New adaptive artificial viscosity method for hyperbolic systems of conservation laws
Journal of Computational Physics
Hi-index | 31.45 |
Adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result. This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific application. The compressible Euler equations are solved with a discontinuous Galerkin method. Time integration is done with an IMEX-method and the dynamic grid adaptivity uses space filling curves via the AMATOS function library. So far the model is able to simulate dry flow in two-dimensional geometry without subgrid-scale modeling. The model is tested with three standard test cases. An error indicator is introduced for a warm air bubble test case which allows one to compare the accuracy between different choices of refinement regions without knowing the exact solution. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. For the rising warm air bubble the additional error by using adaptivity is smaller than 1% of the total numerical error if the average number of elements used for the adaptive simulation is about a factor of two times smaller than the number used for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost two times faster than the uniform simulation. Furthermore the adaptive simulation is more accurate than a uniform simulation when both use the same CPU-time.