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Professor Munz and his group have been working for many years in the development of numerical methods for flow problems and wave propagation.
The current research objectives focus on the construction of high order schemes for several mathematical models in computational engineering. While for ordinary differential equations high order schemes are quite common there is still a lack of efficient methods for partial differential equations. In computational fluid dynamics (CFD) high order accuracy provides more efficient schemes that are capable of capturing small scale phenomena such as turbulent flow or boundary layers. So-called ADER (Arbitrary order using DERivatives) schemes have been developed in which arbitrary order in space and time is achieved. This can be done within the usual finite volume framework. For the discretization of complex geometries the ADER approach has also been successfully extended to Discontinuous Galerkin schemes resulting in methods that achieve high order in space and time on unstructured grids. The results are still highly accurate for heavily distorted grids. The above methods are currently applied to the simulation of
turbulent flow, noise generation and shock-boundary layer interaction. The ADER-DG (ADER – Discontinuous Galerkin) methods are currently developed for solving general two- and three-dimensional linear hyperbolic systems with variable coefficients and source terms. For noise propagation in flow fields and to the near far field we develop numerical algorithms of high accuracy in space and time. These schemes are able to approximate acoustic waves over long distances without significant dispersion and dissipation errors. The main applications are noise generation of flow in aerospace engineering, e.g., turbo machines or high lift devices for airfoils. The coupling of flow with electro-magnetic wave propagation is also being considered for various applications. The high order methods are being applied to the nonstationary Maxwell equations as well as to the magneto hydrodynamic equations. The mathematical and numerical modelling for the simulation of pulsed plasma thrusters for satellites is also under investigation. In this case, the medium can not longer considered as a continuum, i.e., a fluid. Particlein- cell methods are under development which calculate the movement of macro particles in phase space, while the electromagnetic fields are approximated by finite volume schemes on a spatial grid. Several applications of the methods mentioned above are still challenges in high performance computing. Research in this area is done in cooperation with the high performance computing center (HLRS) of Stuttgart University.
Professor Munz and his group have been working for many years in the development of numerical methods for flow problems and wave propagation.
The current research objectives focus on the construction of high order schemes for several mathematical models in computational engineering. While for ordinary differential equations high order schemes are quite common there is still a lack of efficient methods for partial differential equations. In computational fluid dynamics (CFD) high order accuracy provides more efficient schemes that are capable of capturing small scale phenomena such as turbulent flow or boundary layers. So-called ADER (Arbitrary order using DERivatives) schemes have been developed in which arbitrary order in space and time is achieved. This can be done within the usual finite volume framework. For the discretization of complex geometries the ADER approach has also been successfully extended to Discontinuous Galerkin schemes resulting in methods that achieve high order in space and time on unstructured grids. The results are still highly accurate for heavily distorted grids. The above methods are currently applied to the simulation of
turbulent flow, noise generation and shock-boundary layer interaction. The ADER-DG (ADER – Discontinuous Galerkin) methods are currently developed for solving general two- and three-dimensional linear hyperbolic systems with variable coefficients and source terms. For noise propagation in flow fields and to the near far field we develop numerical algorithms of high accuracy in space and time. These schemes are able to approximate acoustic waves over long distances without significant dispersion and dissipation errors. The main applications are noise generation of flow in aerospace engineering, e.g., turbo machines or high lift devices for airfoils. The coupling of flow with electro-magnetic wave propagation is also being considered for various applications. The high order methods are being applied to the nonstationary Maxwell equations as well as to the magneto hydrodynamic equations. The mathematical and numerical modelling for the simulation of pulsed plasma thrusters for satellites is also under investigation. In this case, the medium can not longer considered as a continuum, i.e., a fluid. Particlein- cell methods are under development which calculate the movement of macro particles in phase space, while the electromagnetic fields are approximated by finite volume schemes on a spatial grid. Several applications of the methods mentioned above are still challenges in high performance computing. Research in this area is done in cooperation with the high performance computing center (HLRS) of Stuttgart University.
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COMPUTERS & FLUIDS (2024): 106124-106124
Journal of Fluids and Structures (2023): 103950-103950
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High Performance Computing in Science and Engineering '21pp.305-320, (2023)
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J. Open Source Softw.no. 82 (2023): 4683-4683
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arXiv (Cornell University) (2023)
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High Performance Computing in Science and Engineering '21pp.289-304, (2023)
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J. Sci. Comput.no. 2 (2023): 1-41
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