Truncation Error-Based Anisotropic p-Adaptation for Unsteady Flows for High-Order Discontinuous Galerkin Methods

Resumen

We extendthe tau-estimation method to unsteady problems and use it to adapt the polynomial degree for high-order discontinuous Galerk in simulations of unsteady flows. The adaptation is local and anisotropic and allows capturing relevant unsteady flow features while enhancing the accuracy. We first revisit the definition of the truncation error, studying the effect of the treatment of the mass matrix. Secondly, we extend the tau-estimation strategy to unsteady problems. Finally, we present and compare two adaptation strategies for unsteady problems: the dynamic and static methods. We test the efficiency of the p-adaptation strategies with unsteady two-dimensional simulations using the Euler and Navier-Stokes equations. Since the method relies on the exponential convergence of the scheme, we focus in laminar test cases. The adaptation methods enable reductions in the number of degrees of freedom with respect to uniform refinement, leading to speed-ups of up tox4.5 and x4.5 for Euler and Navier-Stokes.