Numerical Methods for Multimaterial and Multiphase Flows

9973291本提案涉及可压缩多材料和多相流算法的开发和实现。 在这两种类型的流动中，一个主要的数值绊脚石是正确地解释流体组分之间的热力学松弛过程和平衡。 不这样做是最先进的单流体算法通常不适用于多流体流的原因。 Karni是第一个意识到强大的多流体算法的关键是对压力场的良好控制的人之一，并且一直积极开发和实施复杂多材料流的算法。 提出：（i）发展具有表面张力的刚性流体的多物质算法。 数值问题，如刚度，奇异源处理，接口锐化和有效的时间积分将进行研究。 振荡气泡的渐近理论和实验的比较将进行;（ii）多材料算法扩展到多相流模型，特别是2-速度2-压力多相模型，这是足够的一般性和时间双曲线。 数值方面，如全球保护，积极性，有效的整合刚性源项将得到解决。 这些方法将根据数值基准测试进行验证。(iii)使用多材料计算，通过数值平均来"验证"多相流模型。研究平均流动特性可能提供数值Hugoniot曲线的多相（非保守）系统，并可能揭示有争议的问题的本构封闭。 这一部分将与H.M.合作完成。多物质流和多相流是由几种“纯”气体或液体成分组成的流。 例如，氢气和空气，水中的空气，空气中的液滴甚至空气中的灰尘。 根据应用，兴趣可能是跟随分离不同流体的界面的运动，并研究其动力学和稳定性。 例如，计算水中振荡气泡的动力学对于理解水下声波的传播和研究水下爆炸是有用的。 为了在燃烧室中有效地燃烧燃料，人们需要了解混合过程，而混合过程又由空气中的氢气射流的动力学控制。 在其他一些应用程序中，接口的数量可能是巨大的，并且跟踪单个接口的动态不仅是不可能的，而且也是没有意义的。例如，在诸如汽水罐的气泡液体中，在诸如喷雾或含尘气体的液体悬浮液中，单个气泡或液滴的运动是不感兴趣的。 相反，兴趣在于理解流体混合物的“平均”行为。 这两种类型的流动导致需要在计算机上求解的数学模型，并且计算非常密集。 它们也不容易计算。“平均”模型在数学上也不太好理解。 实验虽然可以进行，但很难进行，并受到仪器准确性及其往往很大的误差幅度的限制。 因此，计算机模拟提供了一种补充工具，可以揭示和洞察感兴趣的复杂问题。 在过去的几年里，人们对开发适合于计算多物质/多相流的方法以及有效地实现对复杂流动现象的研究越来越感兴趣。 本项目涉及进一步发展和实施这些方法。

9973291This proposal concerns the development and implementation of algorithms for compressible multimaterial and multiphase flows. In both types of flows, a major numerical stumbling block is accounting correctly for thermodynamical relaxation processes and equilibrium between the fluid components. Failure to do so is the reason why state-of-the-art single fluid algorithms often do not work in multifluid flows. Karni was among the first to realize that the key to robust multifluid algorithms is good control over the pressure field, and has been active in developing and implementing algorithms for complex multimaterial flows. It is proposed: (i) to develop multimaterial algorithms for stiff fluids with surface tension. Numerical issues such as stiffness, singular source treatment, interface sharpening and efficient time integration will be studied. Comparison with asymptotic theories and experiments of oscillating bubbles will be conducted; (ii) to extend multimaterial algorithms to multiphase flow models, in particular to the 2-velocity 2-pressure multiphase model which is sufficiently general and is time hyperbolic. Numerical aspects such as global conservation, positivity, efficient integration of stiff source terms will be addressed. The methods will be validated against numerical benchmark tests. (iii) to use multimaterial computations to 'validate' multiphase flow models by numerical averaging. Studying mean flow properties might provide numerical Hugoniot curves for the multiphase (nonconservative) systems, and might shed light on the controversial issue of constitutive closures. This part will be done in collaboration with H.M. Glaz of the University of Maryland.Multimaterial and multiphase flows are flows consisting of several 'pure' gas or liquid components. For example, hydrogen and air, air in water, liquid droplets in air or even dust in air. Depending on the application, the interest may be to follow the motion of the interface that separates the different fluids and study its dynamics and stability. For example, computing the dynamics of a an oscillating gas bubble in water is useful for understanding the propagation of sound waves underwater, and for studying underwater explosions. In order to burn fuel efficiently in combustion chambers one needs to understand mixing processes, which in turn are governed by the dynamics of, say, a hydrogen jet in air. In some other applications, the number of interfaces may be huge and following the dynamics of individual interfaces is not only impossible but is also not interesting. For example, in bubbly liquids such as soda cans, in liquid suspensions such as in sprays or in dusty gases, the motion of a single bubble or droplet is not of interest. Rather, the interest is in understanding how the fluid mixture behaves 'on average'. Both types of flows lead to mathematical models that need to be solved on computers, and are computationally very intensive. They are also not easy to compute. The 'average' models are also mathematically less well understood. Experiments, while available, are difficult to conduct and are restricted by the accuracy of the instruments and their often large margins of error. Computer simulations provide therefore a complementary tool which may shed light and give insight into the complex problems of interest. The past few years have seen a growing interest in developing methods suitable for computing multimaterial/multiphase flows and in their efficient implementation to studying complex flow phenomena. This project concerns further development and implementation of such methods.