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Not All Numerical Methods are Born Equal for LES
Posted Mon December 17, 2018 @06:35PM
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News Prof. ZJ Wang has posted an article comparing numerical methods for Large Eddy Simulation.

Among the insights shared: "The ideal numerical method for LES should have very low dissipation AND dispersion errors over the resolvable range of wave numbers, but dissipative for non-resolvable high wave numbers. In this way, the simulation will resolve a wide turbulent spectrum, while damping out the non-resolvable small eddies to prevent energy pile-up, which can drive the simulation divergent."


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We want to emphasize the equal importance of both numerical dissipation and dispersion, which can be generated from both the space and time discretizations. It is well-known that standard central finite difference (FD) schemes and energy-preserving schemes have no numerical dissipation in space. However, numerical dissipation can still be introduced by time integration, e.g., explicit Runge-Kutta schemes.

We recently analysed and compared several 6th-order spatial schemes for LES: the standard central FD, the upwind-biased FD, the filtered compact difference (FCD), and the discontinuous Galerkin (DG) schemes, with the same time integration approach (an Runge-Kutta scheme) and the same time step. The FCD schemes have an 8th order filter with two different filtering coefficients, 0.49 (weak) and 0.40 (strong). We first show the results for the linear wave equation with 36 degrees-of-freedom (DOFs) in Figure 1. The initial condition is a Gaussian-profile and a periodic boundary condition was used. The profile traversed the domain 200 times to highlight the difference.

Figure 1
Figure 1. Comparison of the Gaussian profiles for the DG, FD, and CD schemes

Read the full article here.

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