Compressible flow simulation with moving geometries using the Brinkman penalization in high-order Discontinuous Galerkin

Neda Ebrahimi Pour,Nikhil Anand,Harald Klimach,Sabine Roller

doi:10.1186/s40323-021-00195-4

Neda Ebrahimi Pour, Nikhil Anand + Show 2 more

Open Access

https://doi.org/10.1186/s40323-021-00195-4

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Abstract

In this work we investigate the Brinkman volume penalization technique in the context of a high-order Discontinous Galerkin method to model moving wall boundaries for compressible fluid flow simulations. High-order approximations are especially of interest as they require few degrees of freedom to represent smooth solutions accurately. This reduced memory consumption is attractive on modern computing systems where the memory bandwidth is a limiting factor. Due to their low dissipation and dispersion they are also of particular interest for aeroacoustic problems. However, a major problem for the high-order discretization is the appropriate representation of wall geometries. In this work we look at the Brinkman penalization technique, which addresses this problem and allows the representation of geometries without modifying the computational mesh. The geometry is modelled as an artificial porous medium and embedded in the equations. As the mesh is independent of the geometry with this method, it is not only well suited for high-order discretizations but also for problems where the obstacles are moving. We look into the deployment of this strategy by briefly discussing the Brinkman penalization technique and its application in our solver and investigate its behavior in fundamental one-dimensional setups, such as shock reflection at a moving wall and the formation of a shock in front of a piston. This is followed by the application to setups with two and three dimensions, illustrating the method in the presence of curved surfaces.

Highlights

In engineering applications we are often dealing with moving parts
In this work we look into a method to realize moving obstacles in simulations with a high-order discontinuous Galerkin scheme
As with the shock reflection in the previous section we find that the high order can properly handle both the moving geometry and the discontinuity in the solution

Summary

Introduction

In engineering applications we are often dealing with moving parts. When investigating the fluid motion in those scenarios, we need to consider complex, moving obstacles that influence or even drive the flow. We compare the simulation results with the penalization method and moving walls to numerical results with a traditional fixed wall boundary condition and a high resolution This reference is computed with the same element length, but the domain ends at x = 0.5, which is the final position of the wall after t = 0.5 seconds, with a wall boundary condition and a maximal polynomial degree of 255 is used (256 degrees of freedom per element) to approximate the smooth solution. This one-dimensional setup is well studied in literature [19] and the exact solution for the inviscid equations is known For this simulation we use a rigid rectangular piston, modeled by the Brinkman penalization and moving with velocity vp = 150 in a one-dimensional domain.

Conclusion

Findings

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