Abstract
An adaptive spectral/hp discontinuous Galerkin method for the two-dimensional shallow water equations is presented. The model uses an orthogonal modal basis of arbitrary polynomial order p defined on unstructured, possibly non-conforming, triangular elements for the spatial discretization. Based on a simple error indicator constructed by the solutions of approximation order p and p-1, we allow both for the mesh size, h, and polynomial approximation order to dynamically change during the simulation. For the h-type refinement, the parent element is subdivided into four similar sibling elements. The time-stepping is performed using a third-order Runge-Kutta scheme. The performance of the hp-adaptivity is illustrated for several test cases. It is found that for the case of smooth flows, p-adaptivity is more efficient than h-adaptivity with respect to degrees of freedom and computational time.
Original language | English |
---|---|
Journal | International Journal for Numerical Methods in Fluids |
Volume | 67 |
Issue number | 11 |
Pages (from-to) | 1605-1623 |
Number of pages | 19 |
ISSN | 0271-2091 |
DOIs | |
Publication status | Published - 20 Dec 2011 |
Externally published | Yes |
Keywords
- Adaptivity
- Discontinuous Galerkin method
- High-order
- Non-conforming elements
- Shallow water equations