On the performance of the DG method with a directional do-nothing boundary condition

Abstract

We present two numerical experiments concerning application of a recent outflow boundary condition proposal, by Dong et al. (J Comput Phys 261:83-105, 1), to discontinuous Galerkin method (DG) solution of incompressible laminar flows. This new boundary condition (BC) is tailored out for outflow boundaries and its rationale is based on energy influx control at this boundary surface, as described in Braack and Mucha (J Comput Math 32(5):507-521, 2). The authors applied it to various incompressible test-flow examples in a spectral and classic finite-element contexts, and a major result achieved by them was this new outflow boundary's approach allows us to significantly reduce computational domain size without generating significant errors. Accordingly, due to its already known capabilities and established mathematical basis, it is a natural issue to ask about the DG behaviour over this all-useful achievement. In this work, the DG method is tested in two different flow instances: (1) Kovasznay flow, where convergence rates are measured and (2) laminar incompressible flow around cylinder inside rectangular channel. In this case, drag and lift coefficients are computed, further of the dimensionless Strouhal number. Conclusions are traced to show the readiness of DG to embody this new boundary condition technique. Keywords High-order method Á Outflow boundary condition Á Unstructured grids Á Incompressible Navier-Stokes equations Á Discontinuous Galerkin Method

Artificial Far-Field Pressure Boundary Conditions for Wall-Bounded Stratified Flows

“…The first series of results, shown in the figures 2 and 3, was obtained using the new pressure boundary condition (9). The wavy flow pattern generated by the hill is well represented by the isosurfaces of the vertical velocity component shown in the left part of the figure 2, where the regions or ascending/descending flow can easily be identified.…”