Nonlinear Transient Field Problems with Phase Change using the Boundary Element Method

Peer reviewe

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC

Estimating numerical errors due to operator splitting in global atmospheric chemistry models: Transport and chemistry

We present upper bounds for the numerical errors introduced when using operator splitting methods to integrate transport and non-linear chemistry processes in global chemical transport models (CTM). We show that (a) operator splitting strategies that evaluate the stiff non-linear chemistry operator at the end of the time step are more accurate, and (b) the results of numerical simulations that use different operator splitting strategies differ by at most 10 percent, in a prototype one-dimensional non-linear chemistry-transport model. We find similar upper bounds in operator splitting numerical errors in global CTM simulations

Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio

Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the pressure correction has to be solved at every time step in a thin spherical shell representing the global atmosphere. This elliptic solve can be one of the computationally most demanding components in semi-implicit semi-Lagrangian time stepping methods which are very popular as they allow for larger model time steps and better overall performance. With increasing model resolution, algorithmically efficient and scalable algorithms are essential to run the code under tight operational time constraints. We discuss the theory and practical application of bespoke geometric multigrid preconditioners for equations of this type. The algorithms deal with the strong anisotropy in the vertical direction by using the tensor-product approach originally analysed by B\"{o}rm and Hiptmair [Numer. Algorithms, 26/3 (2001), pp. 219-234]. We extend the analysis to three dimensions under slightly weakened assumptions, and numerically demonstrate its efficiency for the solution of the elliptic PDE for the global pressure correction in atmospheric forecast models. For this we compare the performance of different multigrid preconditioners on a tensor-product grid with a semi-structured and quasi-uniform horizontal mesh and a one dimensional vertical grid. The code is implemented in the Distributed and Unified Numerics Environment (DUNE), which provides an easy-to-use and scalable environment for algorithms operating on tensor-product grids. Parallel scalability of our solvers on up to 20,480 cores is demonstrated on the HECToR supercomputer.Comment: 22 pages, 6 Figures, 2 Table