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.

可压缩多相流的数值模拟对于许多数值方法来说都极具挑战性。除其他原因外，这是由于所出现的溶液固有的多尺度特征、尖锐界面的快速移动、流体性质的大幅跃变以及界面力（例如表面张力）的存在。最近，间断伽辽金方法在各种类型的单相流中引起了广泛关注，特别是因为在非常一般的条件下可以实现非常高的收敛速度。然而，现有的多相流扩展通常会回退到相界面附近的低收敛阶，以提高方法的稳定性并避免在用更高的逼近不连续函数时不可避免地发生的非物理振荡。阶多项式。因此，该项目的目标是通过在多项式逼近空间中引入细胞局部的非平滑富集来克服这些问题。由于不连续性的位置是从水平集函数的零等值线推断出来的，因此富集的构造非常简单且高效。凭借一种新颖的求积技术，避免了显式重建界面的必要性，可以以 hp 精度有效地计算诱导子域上的积分。与此同时，丰富的引入意味着主要的挑战，尤其是在稳定性和时间步长方案方面，这将被视为当前项目需要解决的关键问题。相关项目的第一个结果表明，上述技术已在不可压缩多相流的背景下使用，表明它非常适合克服上述限制。上述项目基于BoSSS框架，该框架也将作为当前项目的基础，从而实现密切合作。在这个项目中，我们将完善新方法并将其应用于包含至少一种可压缩物质的流动。我们特别感兴趣的是在表面张力影响下模拟孤立空化气泡的破裂。我们的合作伙伴将在相应的装置上进行实验，并将结果作为验证我们结果的基础。此外，我们的中期目标是实现一个强大且可扩展的求解器，可用于后续项目。