求解扩散方程的一种结合图像的浸入边界方法
An image-incorporated immersed boundary method for diffusion equations
摘要：
提出了一种新的基于尖界面鬼胞的浸入边界方法，并针对扩散问题的解析模型对其参数进行了优化。建议的嵌入式约束移动最小二乘（ECMLS）算法最大限度地减少了误差的插值浓度的图像点的鬼点通过应用移动最小二乘方法对所有内部节点，鬼图像点附近，并通过相应的边界条件，这些内部节点的相关镜像点。使用分析模型作为参考，ECMLS算法相比，约束移动最小二乘（CMLS）算法和阶梯模型，使用各种网格大小，插值基函数，权函数，和罚参数的约束。结果发现，使用ECMLS算法在研究扩散应用中，不完全四次基函数产生最佳性能，而二次，三次和双三次基函数也产生比阶梯模型更好的结果。研究还发现，在扩散应用中，线性和双线性基函数不能产生比阶梯模型更好的结果。结果表明，用于插值的内部节点区域的最佳半径与边界曲率半径的对数曲率半径成比例。结果表明，对于扩散的应用，建议ECMLS算法产生较低的误差在边界上具有更好的数值稳定性在更广泛的范围内的基函数，权函数，边界曲率半径，和罚参数比CMLS算法。
英文摘要：
A novel sharp interface ghost-cell based immersed boundary method has been proposed and its parameters have been optimized against an analytical model in diffusion applications. The proposed embedded constrained moving least-squares (ECMLS) algorithm minimizes the error of the interpolated concentration at the image point of the ghost point by applying a moving least-squares method on all internal nodes, near the ghost image point, and the associated mirrored image points of these internal nodes through the corresponding boundary conditions. Using an analytical model as a reference, the ECMLS algorithm is compared to the constrained moving least-squares (CMLS) algorithm and the staircase model using various grid sizes, interpolation basis functions, weight functions, and the penalty parameter of the constraint. It is found that using ECMLS algorithm in the investigated diffusion application, the incomplete quartic basis function yields the best performance while the quadratic, cubic, and bicubic basis functions also produce results better than the staircase model. It is also found that the linear and bilinear basis functions cannot produce results better than the staircase model in diffusion applications. It is shown that the optimal radius of the region of internal nodes used for interpolation scales with the logarithm of the boundary radius of curvature. It is shown that for the diffusion application, the proposed ECMLS algorithm produces lower errors at the boundary with better numerical stability over a wider range of basis functions, weight functions, boundary radius of curvature, and the penalty parameter than the CMLS algorithm.
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。
