Discontinuous Galerkin methods for incompressible multi-phase flows

在许多技术应用中，例如在内燃机或涡轮机中，多相流扮演着重要的角色。这些流动包含至少两种不同的液体或气体，例如水中的油或空气中的水。技术上相关的例子有通过喷射喷嘴或液膜破碎使液体燃料雾化；其他领域如蒸发过程。这种流动的数值模拟仍然是一个活跃的研究课题。尤其是速度场和压力场中密度跃迁和隐含不连续性的数值表示具有挑战性。在这个项目中，将开发基于不连续Galerkin(DG)方法的多相解。DG方法将在某种程度上进行扩展，以便它能够表示数值单元内的密度跃迁。这样，原DG方法的高精度(即高误差收敛阶)可以扩展到多相流问题。扩展的DG方法的基本成分已经在BOSS中实现；在项目的第一部分，将实现两个不同时间离散化方案的多相流求解器。我们提出了一种基于SIMPLE的多相法和一种基于投影法的多相法。该项目的第二部分涉及第一部分中开发的方法的性能优化。其中包括算法的优化以及软件的优化。特别是，我们计划将BOSS代码的计算代价高昂的部分移植到越来越流行的高性能计算的图形处理单元(GPU)中，在项目的第三部分，应该模拟一些相关的应用程序。这包括，例如，主喷流破碎(喷嘴喷射器)、液滴动力学和预混燃烧。

In many technical applications, for instance in internal combustion engines or turbines, multi-phase flows play an important role. These are flows containing at least two different liquids or gases which do not dissolve, for instance oil in water or water in air. Technically relevant examples are the atomization of liquid fuels by injection nozzels or liquid sheet breakup; other areas are e.g. evaporation processes.The numerical simulation of such flows is still an actively researched topic. Especially the numerical representation of the density jump and the implied discontinuities in the velocity and pressure field are numerically challenging.Within this project, multi-phase solvers which are based on the discontinuous Galerkin (DG) method will be developed. The DG method will be extended in a way so that it is capable of representing the density jump within a numerical cell. By doing so, the high precision (i.e. the high error convergence order) of the original DG method could be extended to multi-phase flow problems.The basic ingredients of the extended DG method have already been implemented in BoSSS; within the first part of the project, two multi-phase flow solvers with different time discretization schemes will be implemented. We suggest one multi-phase method that is based on SIMPLE and another one which is based on the projection method. The second part of the project addresses the performance-optimization of the methods which have been developed in the first part. These include an optimization of the algorithms as well as software-optimization. Especially, we plan to port computationally expensive parts of the BoSSS-code to so-called `Graphics Processing Units’ (GPU’s) which are becoming more and more popular for high-performance computing.Within the third part of the project, some relevant applications should be simulated. This includes, for instance, primary jet breakup (nozzle injectors), droplet dynamics and premixed combustion.