非线性系统
接口(物质)
流离失所(心理学)
二次方程
数学分析
能量(信号处理)
散射
工作(物理)
应用数学
机械
计算机科学
数学优化
数学
物理
光学
几何学
气泡
心理治疗师
最大气泡压力法
统计
热力学
量子力学
心理学
作者
Michael D. Collins,William L. Siegmann
摘要
Several approaches are being investigated for improving the elastic parabolic equation for problems involving sloping fluid-solid interfaces. Approaches based on single scattering and energy conservation provide accurate solutions for problems involving sloping fluid-fluid and solid-solid interfaces, but the mixed-media problem has proven to be more challenging. The energy-conservation approach has been applied previously by deriving a linear equivalent to the nonlinear expression for energy flux. One of the approaches that are currently being investigated is based on going back to the nonlinear expression. Although it would not be practical to solve the full nonlinear scattering problem, promising results have been obtained for the fluid-fluid case with this approach by correcting the amplitude at only one grid point near the interface. With this approach, the nonlinear problem reduces to the evaluation of a quadratic function. Another approach that is being investigated is based on an alternative formulation that involves the vertical displacement and a quantity that is proportional to the normal stress on a horizontal interface. In these variables, the interface conditions across a horizontal interface are first order, and this may facilitate the extension of the single-scattering solution to the mixed-media problem. [Work supported by the Office of Naval Research.]
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