Baer-Nunziato两相流模型的一种熵稳定高阶间断伽辽金谱元方法
An entropy stable high-order discontinuous Galerkin spectral element method for the Baer-Nunziato two-phase flow model
AI总结：
提出一种基于DGSEM和SBP算子的熵稳定高阶格式求解Baer-Nunziato两相流模型，通过熵守恒波动通量和界面熵稳定通量保证半离散熵不等式，并保持动能与正性，数值实验验证了精度和鲁棒性。
摘要：
本文针对Baer-Nunziato两相流模型（Baer和Nunziato，Int. J. Multiphase Flow, 12 (1986), pp. 861-889）提出了一种高阶离散方法，其中界面速度和压力的闭合关系适用于不连续解的处理，并采用了刚性气体状态方程。我们使用基于求积和插值点配置的间断伽辽金谱元方法（DGSEM）（Kopriva和Gassner，J. Sci. Comput., 44 (2010), pp. 136-155）。DGSEM在数值求积中使用求和-by-部分（SBP）算子来近似离散单元上的积分（Carpenter等，SIAM J. Sci. Comput., 36 (2014), pp. B835-B867；Gassner等，J. Comput. Phys., 327 (2016), pp. 39-66）。在此，我们基于F. Renac（J. Comput. Phys., 382 (2019), pp. 1-36）为非守恒双曲系统提供的框架，使用SBP算子修改单元上的积分，并将物理通量替换为Castro等人（SIAM J. Numer. Anal., 51 (2013), pp. 1371-1391）的熵守恒波动通量，同时我们推导了在界面处应用的熵稳定通量。这使得我们能够建立单元平均物理熵的半离散不等式，同时保持高阶精度。数值通量的设计还在半离散水平上正式保持了动能。时间上的高阶积分采用强稳定性保持龙格-库塔格式，我们提出了数值参数的条件以确保单元平均空隙率和部分密度的正性。单元平均解的正性通过使用后验限制器扩展到节点值。通过在一维和二维空间中的多个数值实验，评估了本方案的高阶精度、非线性稳定性和鲁棒性。
英文摘要：
In this work we propose a high-order discretization of the Baer-Nunziato two-phase flow model (Baer and Nunziato, Int. J. Multiphase Flow, 12 (1986), pp. 861-889) with closures for interface velocity and pressure adapted to the treatment of discontinuous solutions, and stiffened gas equations of states. We use the discontinuous Galerkin spectral element method (DGSEM), based on collocation of quadrature and interpolation points (Kopriva and Gassner, J. Sci. Comput., 44 (2010), pp. 136-155). The DGSEM uses summation-by-parts (SBP) operators in the numerical quadrature for approximating the integrals over discretization elements (Carpenter et al., SIAM J. Sci. Comput., 36 (2014), pp. B835-B867; Gassner et al., J. Comput. Phys., 327 (2016), pp. 39-66). Here, we build upon the framework provided in (F. Renac, J. Comput. Phys., 382 (2019), pp. 1-36) for nonconservative hyperbolic systems to modify the integration over cell elements using the SBP operators and replace the physical fluxes with entropy conservative fluctuation fluxes from Castro et al. (SIAM J. Numer. Anal., 51 (2013), pp. 1371-1391), while we derive entropy stable fluxes applied at interfaces. This allows to establish a semi-discrete inequality for the cell-averaged physical entropy, while being high-order accurate. The design of the numerical fluxes also formally preserves the kinetic energy at the semi-discrete level. High-order integration in time is performed using strong stability-preserving Runge-Kutta schemes and we propose conditions on the numerical parameters for the positivity of the cell-averaged void fraction and partial densities. The positivity of the cell-averaged solution is extended to nodal values by the use of an a posteriori limiter. The high-order accuracy, nonlinear stability, and robustness of the present scheme are assessed through several numerical experiments in one and two space dimensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
