Higher order accurate simulation of compressible multi-phase flows by means of a Discontinuous Galerkin method with non-smooth basis functions

利用非光滑基函数的间断伽辽金法对可压缩多相流进行高阶精确模拟

基本信息

批准号：
250648477
负责人：
Professor Dr.-Ing. Yongqi Wang
金额：
--
依托单位：
Fachgebiet Strömungsdynamik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2014
资助国家：
德国
起止时间：
2013-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/250648477?language=en
关键词：
Higher order accurate simulation compressible

项目摘要

The numerical simulation of compressible multi-phase flows is extremely challenging for many numerical methods. Among other reasons, this is due to the inherent multi-scale character of the occurring solutions, the rapid movement of the sharp interface, the large jump in fluid properties and the presence of interfacial forces such as the surface tension. Recently, the Discontinuous Galerkin method has gained much attention in the context of various types of single-phase flows, especially because of the remarkably high convergence rates that can be achieved under very general conditions. However, existing extensions to multi-phase flows typically fall back to low convergence orders in the vicinity of the phase interface in order to improve the stability of the method and to avoid non-physical oscillations that inevitably occur if a discontinuous function is approximated by higher order polynomials. As a result, this project is targeted at overcoming these problems by introducing a cell-local, non-smooth enrichment into the polynomial approximation space. Since the location of the discontinuity is inferred from the zero iso-contour of a level set function, the construction of the enrichment is very simple and efficient. By virtue of a novel quadrature technique that avoids the necessity to reconstruct the interface explicitly, integrals over the induced sub-domains can be computed efficiently with hp-accuracy. At the same time, the introduction of the enrichment implies principal challenges, most notably in terms of stability and time-stepping schemes, which will be considered as key issues to be solved in the present project. First results from a related project where the aforementioned technique has been used in the context of incompressible multi-phase flows indicate that it is very well suited for overcoming the above-mentioned limitations. The mentioned project is based on the BoSSS framework which will also serve as a basis for the present project, thus allowing for a close cooperation. Within this project, we will refine the new methodology and apply it to flows comprising at least one compressible species. In particular, we are interested in the simulation of the collapse of isolated cavitation bubbles under the influence of surface tension. Experiments on a corresponding set-up will be performed by our cooperation partners and the results will serve as a basis for the verification of our results. Furthermore, our mid-term goal is the realization of a robust and extensible solver that can be used in follow-up projects.

对于许多数值方法，可压缩多相流的数值模拟极具挑战性。除其他原因外，这是由于发生的溶液的固有多尺度特征，尖锐界面的快速运动，流体特性的大跳跃以及界面力（例如表面张力）的存在。最近，在各种类型的单相流的情况下，不连续的Galerkin方法引起了很多关注，尤其是因为在非常一般的条件下可以达到的收敛速率非常高。但是，多相流的现有扩展通常落后于相位界面附近的低收敛顺序，以提高方法的稳定性，并避免如果不连续函数近似于较高的多项式，则不可避免地会发生这种非物理振荡。结果，该项目的目标是通过将细胞本地的非平滑富集引入多项式近似空间来克服这些问题。由于不连续性的位置是从级别设置函数的零ISO-CONTOUR推断出来的，因此富集的构造非常简单有效。借助一种新型的正交技术，该技术避免了明确重建界面的必要性，可以使用HP准会有效地计算出诱导子域的积分。同时，富集的引入意味着主要挑战，最著名的是在稳定和时间发展方案方面，这将被视为在本项目中要解决的关键问题。相关项目的第一个结果，该项目在不可压缩的多相流中使用了上述技术，这表明它非常适合克服上述限制。提到的项目基于Bosss框架，该框架还将作为本项目的基础，从而可以进行密切合作。在该项目中，我们将完善新方法，并将其应用于包含至少一个可压缩物种的流。特别是，我们对在表面张力的影响下模拟分离的气泡气泡的崩溃感兴趣。我们的合作伙伴将对相应的设置进行实验，结果将作为验证我们结果的基础。此外，我们的中期目标是实现可在后续项目中使用的坚固且可扩展的求解器。