Mathematical Sciences: Investigation of Rayleigh-Taylor Flow

这一建议涉及两种不同密度流体之间的界面运动，当较重的流体最初停留在较轻的流体上（瑞利-泰勒流）。当传统的数值方法由于分辨率问题而难以解决时，将采用分析和数值技术相结合的方法来跟踪高度卷曲界面的后期运动。该方法依赖于实际跟踪奇异点在非物理领域的运动，当它们接近物理领域时对应于界面特征，如尖峰。通过在物理域的基表示中减去这种奇异点，提出了连续畸变瑞利-泰勒界面的数值计算方法。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，惯性约束装置试图通过磁场限制热等离子体并实现受控核聚变以满足能量需求。因为加速场和引力场是等价的，等离子体在旋转时的径向加速度使它容易受到这种不稳定性的影响。很明显，要使等离子体约束成功，就必须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。该攻击方法新颖，是对传统数值方法不足的一种尝试。

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.