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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是极具挑战性的。除其他原因外，这是由于所出现的解决方案的固有多尺度特性、尖锐界面的快速移动、流体性质的大幅跳跃以及界面力（例如表面张力）的存在。最近，不连续Galerkin方法在各种类型的单相流的背景下获得了很大的关注，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，现有的扩展到多相流通常回落到相界面附近的低收敛阶，以提高该方法的稳定性，并避免非物理振荡，不可避免地发生，如果一个不连续的函数近似高阶多项式。因此，该项目的目标是克服这些问题，通过引入一个细胞的本地，非光滑的多项式逼近空间的丰富。由于不连续点的位置是由水平集函数的零等值线推断的，因此富集的构造非常简单和有效。凭借一种新的正交技术，避免了显式重建接口的必要性，积分诱导子域可以有效地计算HP精度。与此同时，采用浓缩意味着主要的挑战，最主要的是在稳定性和时间步进计划方面，这将被视为本项目需要解决的关键问题。第一个结果从一个相关的项目中，上述技术已被用于不可压缩的多相流的上下文中表明，它是非常适合于克服上述的限制。上述项目以BoSSS框架为基础，该框架也将作为本项目的基础，从而允许密切合作。在这个项目中，我们将完善新的方法，并将其应用到至少包括一个可压缩的物种流。特别是，我们感兴趣的孤立空化气泡的崩溃的表面张力的影响下的模拟。我们的合作伙伴将在相应的设置上进行实验，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一个强大的和可扩展的求解器，可用于后续项目。