Jens Utzmann

Heterogeneous domain decomposition for computational aeroacoustics

This paper presents a strategy to accelerate the direct simulation of aeroacoustic problems in terms of CPU time. The key idea is to introduce a heterogeneous domain decomposition. The whole computational domain is subdivided into smaller domains. In each of these subdomains the equations, the discretization, the mesh, and the time step may be different and are adapted to the local behavior of the solution. To reduce the total number of elements we propose the use of high order methods. Here the class of arbitrary high-order using derivatives-finite volume schemes on structured meshes and arbitrary high-order using derivatives discontinuous Galerkin methods on unstructured meshes seem a good choice to us. The coupling procedure is validated and numerical results for the interface transmission problem and the single airfoil gust response problem (from 4th Computational Aeroacoustics Workshop on Benchmark Problems, CP-2004 212954, NASA, 2004) are presented, together with the acoustic scattering problem at a cylinder and at multiple objects. The coupling approach proves to be especially efficient for the propagation of sound in large domains.

Aeroacoustic Simulations for Complex Geometries based on Hybrid Meshes

This paper advances the idea of a heterogeneous domain decomposition for Computational Aeroacoustics (CAA). Direct simulations of aeroacoustic problems are accelerated by sub-dividing the computational domain into smaller domains. In each of these subdomains the equations, the discretization, the mesh and the time step may be different and are adapted to the local behavior of the solution. High order methods such as ADER-Finite Volume and ADER-Discontinuous Galerkin methods are used to reduce the total number of elements and to ensure good wave propagation properties. Here, we add a high order Finite Difference method to the acoustic solvers and integrate it into the coupling framework. The new scheme shows good performance properties for the convective transport of a Gaussian pulse in density. In the examples section, convergence rates for the coupling procedure in 3D show that high order of accuracy is maintained globally also for partitioned domains. A numerical example that involves multiple domains underlines the flexibility of the approach. Another example shows that the proposed domain decomposition also holds for the coupling of the Navier-Stokes equations with the Linearized Euler Equations.

Fluid-Acoustic Coupling and Wave Propagation

Different strategies regarding the simulation of sound generation and propagation are explored. A hydrodynamic/acoustic splitting method for computational aeroacoustics in low Mach number flows with variable density, temperature gradients and heat conduction is described. The resulting equations can be formulated as linearized Euler equations plus source terms and reduce to the linear acoustic wave equation, if convection speeds can be neglected. In contrast, a direct approach based on the coupling of different grids, time steps and equations allows a simulation of both flow and acoustics in one single calculation. For acoustic domains, the ADER discontinuous Galerkin and the conforming face finite element discretizations are efficient high order methods for unstructured grids. The proposed methods are validated and applied to complex test cases such as the simulation of an aero-engine inlet and the scattering of sound waves at a solid sphere.

Heterogeneous Domain Decomposition for Numerical Aeroacoustics

A strategy is presented to accelerate the direct simulation of aeroacoustic problems in terms of computer time. The key idea is to introduce a heterogeneous domain decomposition. The whole computational domain is sub-divided into smaller domains. In each of these sub-domains the equations, the discretization, the mesh and the time step may be different and are adapted to the local behavior of the solution. To reduce the total number of elements we propose the use of high order methods. Here the class of ADER-Finite Volume schemes on structured meshes and ADER-Discontinuous Galerkin methods on unstructured meshes seem a good choice to us. The coupling procedure is validated and numerical results for the Single Airfoil Gust Response Problem from the 4th CAA Workshop on Benchmark Problems are presented, together with the acoustic scattering problem at a cylinder and at multiple objects. The coupling approach proves to be especially efficient for the propagation of sound in large domains.

An Explicit Space-Time Discontinuous Galerkin Scheme with Local Time-Stepping for Unsteady Flows

The objective of our project is the development of high-order methods for the unsteady Euler and Navier Stokes equations. For this, we consider an explicit DG scheme formulated in a space-time context called the Space-Time Expansion DG scheme (STE-DG). Our focus lies on the improvement of two main aspects: Increase of efficiency in the temporal and spatial discretization by giving up the assumption that all grid cells run with the same time step and introducing local time-stepping and the shock capturing property, where we have adopted the artificial viscosity approach as described by Persson and Peraire to our STE-DG scheme. Thus, we try to resolve the shock within a few relatively large grid cells forming a narrow viscous profile by locally adding some amount of artificial viscosity.

Parallel Coupling of Heterogeneous Domains with KOP3D using PACX-MPI

This paper outlines how coupled heterogeneous domains can be distributed in a supercomputing environment using PACX-MPI. KOP3D is a coupling program in the field of aero acoustics, a typical multi-scale application, since on the one hand it has to account for the small vortical structures as the source of the noise and on the other for the long wave length of the acoustic waves. The amount of energy, and with that the pressure, in the sound generating flow is by orders of magnitude higher than the amount of energy carried by the acoustic waves. The acoustical wavelength is much larger than the diameter of the noise-generating vortices, and even the computational domains may vary in a wide range from the geometry which is in the order of meters for an airfoil to the distance between a starting or landing plan and the observer on the ground which is in the order of about 1 km. Through the use of heterogeneous domain decomposition it is possible to reduce the computation time needed to simulate large flow fields by adaptation of the equations, the discretization, the mesh and the time step to the local requirements of the flow simulation within each sub-domain. These locally adapted computations may result in different requirements on the computer architecture. On the other side, in a supercomputing network there are generally different computer architectures available. By matching the sub-domains to the best suited available architectures an even shorter time to solution may be gained. The parallel version of the KOP3D coupling scheme is shown and the benefits of running the simulation distributed on the vector machine NEC-SX8 and on the scalar Itanium II (IA64) machine are demonstrated. A 2D and a 3D testcase are presented.

Domain Decompositions for CAA in Complex Domains

A heterogeneous domain decomposition approach is proposed, which tackles the multiscale problem of sound generation and propagation in Computational Aeroacoustics (CAA). Direct simulations of aeroacoustic problems are accelerated by sub-dividing the computational domain into smaller domains. In each of these sub-domains the equations, the discretization, the mesh and the time step may be different and are adapted to the local physical properties of the solution. High order finite volume, finite difference and discontinuous Galerkin methods are used in order to reduce the total number of elements and to ensure the high resolution of the flow and the acoustics at the same time. In the examples section, the decomposition method is applied to the simulation of a Von Karman vortex street at Re = 150.

Building Blocks for Direct Aeroacoustic Simulations based on Domain Decompositions

The high-order coupling procedure inside a domain decomposition framework is described in detail. Such a framework is used in order to decrease the computational effort of direct simulations for CAA. The coupling mechanism is based on high-order polynomial interpolation. Convergence studies show, that the method is capable of maintaining globally high-order of accuracy. Numerical tests reveal, that reflections at the domain interfaces are negligible. High-frequency waves are naturally filtered out when they enter grids that are too coarse to support the respective wavelengths. A three-dimensional Sphere Scattering benchmark example underlines the efficiency of the domain decomposition approach, especially for far-field computations.

Direct aeroacoustic simulations based on domain decompositions

For CAA, an accurate and feasible direct simulation that considers both the generation of sound within the flow and its propagation into the far‐field is hard to realize with one numerical method in a single computational domain. On the other hand, a direct approach contains automatically the interaction of the acoustic perturbations with the flow‐field, a property which lacks the popular acoustic analogy models. The proposed method is basically a direct simulation, but it simplifies the problem that has to be solved for individual regions in the computational domain. The idea is to use a non‐overlapping domain decomposition method where the equations, methods, grids and even the time steps are adapted to meet the local requirements. Inside the coupling framework, high‐order solvers from different classes of methods are available: On unstructured grids, a reconstructed ADER finite volume method (ADER‐FV) is used for linear and nonlinear problems, as well as a discontinuous Galerkin method. On structured g...