Investigating Coupled Fluid-Structure-Acoustic (FSA) Interaction

**Principal Investigator:**

Harald Klimach

**Affiliation:**

Simulation Techniques and Scientific Computing, University of Siegen

**Local Project ID:**

pr62cu

**HPC Platform used:**

SuperMUC of LRZ

**Date published:**

Within the scope of the ExaFSA project the chair for Simulation Techniques and Scientific Computing (STS) of Prof. Dr. Sabine Roller at the University Siegen investigated the coupling of fluid domains with different properties to allow the simulation of sound generated by flows. The main work in this project was done by the doctoral student Neda Ebrahimi Pour at the chair of Simulation Techniques and Scientific Computing (STS) on HPC system SuperMUC of LRZ in Garching.

Acoustic properties play an increasingly important role in the design of new devices as we get more and more aware of the negative impact of noise and the multitude of utilized machinery in modern society. Sophisticated acoustic simulations can help design machines that avoid noise more easily, and the development of software to that end is accordingly of high interest.

The overall goal of the ExaFSA project was the development of a software environment, that allows for the simulation of sound generated in the vicinity of objects that influence the flow and get influenced by it. This is generally referred to as Fluid-Structure Interaction. The challenge in the direct simulation of acoustics from flows, referred to as aero-acoustics, arises from the vastly different scales that need to be considered, which make it hard to resolve all necessary effects in the numerical approximation.

Turbulent flows that generate sound consist of small vortices with high energy and large pressure variations. Close to the obstacles the viscosity of the fluid also plays a role and needs to be considered as it dissipates kinetic energy into heat. Acoustic waves on the other hand are manifest only in tiny pressure variations that travel with the speed of sound over large distances. Considering also the influence of the fluid on the structure adds another level of complexity. With this compute time project, we concentrated on the fluid part, though. Due to the different regimes that need to be covered by the simulation it is not feasible to use the same discretization for everything. Instead the numerical approach needs to be adapted to the various parts.

Luckily, we usually can distinguish separate spatial areas in aero-acoustic problems. In the vicinity of obstacles, which usually cause the turbulent structures in the flow, small spatial scales are required to resolve the vortices and the viscosity of the fluid needs to be considered. In this domain we need to solve the full compressible Navier-Stokes equations, which describe viscous flows. Far away from any obstacles, however, there are only the acoustic waves that impose small pressure variations over long distances. To describe the transport of these waves, a simpler model can be used. The influence of the viscosity in the flow is negligible and we can even drop the description of vortices and stick with linear wave transport, which is much easier to solve than the nonlinear Navier-Stokes equations.

In between we usually find domains, where the viscosity can be neglected but the vortices still need to be properly modelled. This results in the so called nonlinear inviscid Euler equations. The idea for direct simulation of aero-acoustic problems is to split the overall domain into subdomains and solve each one with the appropriate model and discretization. This enables us to capture both, the small-scale structures of the turbulent flow and the fast transport of small perturbations in the acoustic waves across long distances.

However, this separation introduces the need to couple the individual domains together. Within this compute time project, we are looking at a large scale direct aero-acoustic simulation and various approaches to this coupling. The spatially separated domains in the described method interact with each other at interfaces by providing boundary values to each other. The complication arises now from the desire to utilize resolutions and numerical schemes tailored to the respective phenomena to be resolved. Due to these discrepancies the exchanged data needs to be interpolated at the interfaces.

There are some generic coupling tools available, that enable the interaction of multiple solvers to allow for such multi-physic simulations more easily and take care of the interpolation. In the ExaFSA project we made use of the preCICE library for this coupling. It allows us the combination of our own solver Ateles with other solvers, such as the widespread OpenFOAM. Such a combination is attractive as we want to benefit from the respective advantages. Our solver aims for a high-order discretization, where polynomials of high degree are used to represent the solution. This is well suited for the efficient computation of the sound wave propagation, but our solver does not incorporate fluid-structure interactions. Thus, in ExaFSA the proposal is to use a solver like OpenFOAM for the Navier-Stokes discretization in the vicinity of obstacles, while utilizing the high-order approximation in the domains further out.

This compute time project is a subset of the overall ExaFSA project with the goal to investigate the coupling of the various fluid domains. For this we consider a setup where all domains are solved with the Discontinuous Galerkin solver Ateles albeit with independent discretization, that is, individual choices for mesh size, scheme order and equation to solve in each domain. The problem we solve is a jet that impinges on an airfoil, and we performed several simulations with high resolution of this problem to compare coupling strategies in the context of massively parallel executions.

Besides the generic coupling provided by preCICE, we also looked into a dedicated coupling approach offered in the framework of our solvers, which we refer to as APESmate. While preCICE takes care of the interpolation itself and expects the solver only to provide values at certain points, APESmate leaves the interpolation to the solver. The preCICE approach opens great flexibility and allows for a fairly straight forward incorporation of the coupling in a wide range of solvers.

The approach taken in APESmate on the other hand, allows the interpolation to fully exploit the representation offered by the numerical scheme. Thus, in the Discontinuous Galerkin scheme, where functions are used to represent the solution a more accurate matching can be made by evaluating those functions. The analysis has shown, this is especially important when considering polynomials of high degree as those that we employed for the simulation of sound waves in the far field.

We investigated various interpolation methods offered by preCICE and some variants thereof, the APESmate approach, and in a smaller setup a monolithic simulation where the whole domain is computed with the same discretization and the compressible Navier-Stokes equations are used everywhere. The computational effort, the accuracy and the parallel scalability of the respective methods were compared. We found, that some additional effort needs to be done to prepare the data for coupling by preCICE to obtain good solutions when high scheme orders are employed in the domains. For low-order representations the generic preCICE interpolation methods proofed to be sufficient.

In terms of parallel scalability there was a slight advantage from the APESmate implementation in comparison to the usage of preCICE. All in all, the simulations showed that the partitioned approach works well for this kind of multiscale problems. Both, preCICE and Ateles with APESmate are available as open source to the general public, and we hope that the findings and developments from this project contribute to the capability to accurately simulate aero-acoustic problems.

**Research Team**

Harald Klimach (PI), Neda Ebrahimi Pour

both: Chair of Simulation Techniques and Scientific Computing (STS), University of Siegen

**Scientific Contact**

Dr.-Ing. Harald Klimach

Chair of Simulation Techniques and Scientific Computing (STS)

University of Siegen

Adolf-Reichwein-Straße 2, D-57068 Siegen (Germany)

e-mail: harald.klimach [@] uni-siegen.de

*LRZ Project ID: pr62cu*

*July 2020*