A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

Abstract

A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to develop a model to damp flow disturbances (advective and acoustic) that propagate outside an arbitrarily defined near field. This effectively simulates a free-space boundary condition. Damping the solution in the far field is accomplished in a simple and effective way by applying a filter (similar to that used in large-eddy simulation) on a mesh in Fourier space, followed by a secondary filtering of the equations on the physical grid and implementation of a model for the unresolved scales. The final form of the buffer region is given in real space, independent of any discretization of the equations. Here we use a dealiased, Fourier spectral collocation method to demonstrate the efficacy of the buffer region for several model problems: acoustic wave propagation, convection of a finite-amplitude vortex, and a viscous starting jet in two dimensions. The results compare favorably to previous nonreflecting and absorbing boundary conditions.

A General Perfectly Matched Layer Model for Hyperbolic-Parabolic Systems

“…The case with more stretching gives slightly better results; also it seems that the maximum error does not depend much on the damping parameter, but that errors at later times do. We also compute solutions using Colonius' super grid scale boundary conditions [10] using the same number of points and the same damping functions in the super grid layer. The super grid layer gives a slightly larger error than the proposed layer, but on the other hand requires less memory and CPU.…”

A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems

“…The SuGS model, originally developed for compressible flow, exploits the connection between coordinate mapping from bounded to unbounded domains and the filtering of the equations of motion to construct models that damp disturbances outside the near field. The two building blocks of the SuGS model are reduction of the unbounded domain (by windowing, coordinate transformation, grid stretching or slowing down of waves) and damping of the super-grid scales that cannot be represented on the bounded domain (the name, the super-grid-scale model, was chosen in [1] to convey the analogy with sub-grid modeling in large eddy simulations (LES)). In [1], where compressible flow was considered, the model used for the super-grid scales consisted of a parabolic damping term, motivated by an expansion of a product of filtered fields used in tensor diffusivity models for LES.…”

“…In this paper we continue the development of the super-grid-scale (which we hereafter denote SuGS not to confuse it with sub-grid-stress) framework initiated in [1]. The SuGS model, originally developed for compressible flow, exploits the connection between coordinate mapping from bounded to unbounded domains and the filtering of the equations of motion to construct models that damp disturbances outside the near field.…”

“…As in [1] we reduce unbounded domains by a smooth coordinate transformation. The reduced problem consists of the original problem inside the computational domain, and a variable coefficient problem inside a slowing-down layer.…”

Analysis of sponge zones for computational fluid mechanics

“…Colonius and Ran [13] proposed a super-grid-scale boundary condition based on windowing the governing equations in physical space. Using an approximate form of their model they find superior results compared to PML in an acoustic reflection problem and roughly equivalent performance to the present method in a convecting nonlinear vortex problem.…”