An important trend in Computational Fluid Dynamics is towards high‐order methods, as they offer a substantially lower discretization error for the same number of degrees of freedom (DOF). Examples are the Spectral‐Element Methods (SEM) and Discontinuous Galerkin (DG) methods. Unfortunately, with most implementations the work load of such solvers increases drastically with the number of DOF, for example, when increasing the polynomial degree of the approximation. This issue gets particular pressing for elliptic solvers which are a vital building block in the time‐stepping of the incompressible Navier‐Stokes equations, resulting from pressure projection methods or implicit treatment of viscous terms. So far, this drastic increase of resources has hampered the use of SEM for higher polynomial degrees, such as 16 or more.
Proceedings in Applied Mathematics & Mechanics – Wiley
Published: Jan 1, 2017
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