A three-dimensional finite-volume solver for the Maxwell equations with divergence cleaning on unstructured meshes
Abstract
A finite-volume scheme on unstructured meshes for the three-dimensional time-dependent Maxwell equations is presented. To avoid the increase of numerical errors caused by suppressing the information contained in Gauss' law as well as the divergence-free condition of the magnetic induction, a divergence cleaning step is added which does not require the solution of a Poisson equation. The elliptical constraints of the Maxwell equations is approximated by a hyperbolic condition, starting from the so-called Generalised Lagrange Multiplier Maxwell model. This results in a purely hyperbolic system that fits very well in the framework of high-resolution finite-volume schemes yielding an efficient and flexible parallel Maxwell solver for explicit field calculations in time domain on unstructured grids in three space dimensions. Simulation results obtained with this new approximation technique are presented and compared with analytical as well as with other methods.
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ALPACA - a level-set based sharp-interface multiresolution solver for conservation laws
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Program Title: ALPACA - Adaptive Level-set Parallel Code Alpaca
CPC Library link to program files: https://doi.org/10.17632/5zr3sg83ct.1
Developer's repository link: https://gitlab.lrz.de/nanoshock/ALPACA
Licensing provisions: GPLv3
Programming language: C++20
Supplementary material: Code: Copy of the git repository, Videos: Air-helium shock bubble interaction (front and back view), Air-R22 shock bubble interaction, Three bubble shock interface interaction.
Nature of problem: Numerical simulation of conservation laws such as the compressible Navier-Stokes equation with several interacting gaseous and liquid phases remains challenging even today. These flows often involve singularities such as shocks and interfaces as well as instabilities driven by their interaction. The inherent highly nonlinear dynamics of those systems leads to a broad range of temporal and spatial scales that have to be resolved. There exists a variety of mutually exclusive numerical models that are able to tackle these challenges. Those, however, are computationally expensive and require computational power that is offered only by large-scale state-of-the-art distributed-memory machines.
Solution method: We have developed a modular simulation environment for conservation laws allowing exchange of numerical methods without loss of parallel performance. Computational efficiency is enhanced by employing multi-resolution schemes with adaptive local-time stepping. Our block-based implementation of these schemes is parallelized using the Message Passing Interface and exploits vectorization capabilities of the compute hardware. To simulate distinct and immiscible phases inside the computational domain, we utilize a sharp-interface level-set method. The level-set method allows to accurately locate the interface position and to easily prescribe arbitrary coupling conditions. The narrow-band approach reduces the computational load of the level-set method. We extend this method by a smart tagging system that exploits the block-based nature of the algorithm and further reduces the computational load. The simulation framework is written in modern C++20 and provides a Python interface for integration in Machine Learning and Uncertainty Quantification toolchains. We use parallel HDF5 in combination with XDMF to output field quantities. CMake is used as build system. We have completely annotated the source code using doxygen-style comments, allowing automated documentation generation in different formats. The source code is equipped with CI/CD-automated unit tests and an exhaustive integration test suite.
Additional comments including restrictions and unusual features: ALPACA relies on open-source third-party libraries for input and testing. These are packaged as git submodules and automatically integrated. ALPACA is tested on Linux and macOS.
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