Mathematical Sciences: Investigation of Rayleigh-Taylor Flow

这一建议涉及当较重的流体最初停留在较轻的流体(瑞利-泰勒流动)上时，不同密度的两种流体之间的界面的运动。当传统的数值方法由于求解问题而难以解决时，将采用解析和数值技术相结合的方法来跟踪高度曲折的界面的运动。该方法依赖于实际跟踪非物理域中奇点的运动，这些奇点在接近物理域时对应于诸如尖峰等界面特征。通过从物理域中的基表示中减去这种奇点，提出了用数值方法计算连续扭曲的Rayleigh-Taylor界面。人们对瑞利-泰勒不稳定性的兴趣源于它在惯性约束装置中的破坏性存在，在惯性约束装置中，人们试图通过磁场限制热等离子体，并实现受控的核聚变，以满足能源需求。由于加速场和引力场是等价的，等离子体转动时的径向加速度使其容易受到这种不稳定性的影响。很明显，要使等离子体限制成功，人们应该能够控制这种不稳定性。第一步是了解瑞利-泰勒流的详细性质。这种攻击方法新颖，是克服其他一些传统数值方法缺点的一种尝试。

This proposal concerns the motion of an interface between two fluids of different densities when the heavier fluid initially rests on the lighter fluid (Rayleigh-Taylor flow). A combination of analytical and numerical techniques will be employed to follow the motion of a highly convoluted interface for late times when traditional numerical methods have difficulty because of resolution problems. The method relies on actually following the motion of singularities in the unphysical domain that on their approach to the physical domain correspond to interfacial features such as spikes. By subtracting such singularities from a basis representation in the physical domain, it is proposed to calculate a continually distorting Rayleigh-Taylor interface numerically. Interest in the Rayleigh-Taylor instability stems from its disruptive presence in inertial confinement devices where attempt is made to confine a hot plasma through a magnetic field and achieve controlled nuclear fusion for energy needs. Because an accelerating field and a gravitational field are equivalent, the radial acceleration of a plasma as it turns around makes it susceptible to this instability. It is clear that for plasma confinement to succeed, one should be able to control this instability. A first step is to understand the detailed nature of a Rayleigh-Taylor flow. The method of attack is novel and is an attempt to overcome the shortcomings of some other traditional numerical methods.