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.
翻译:提出了一个以幽灵图像点附近所有内部节点和这些内部节点的相关反射图像点,提出了一种新的尖锐界面幽暗边界法,并且根据扩散应用的分析模型优化了其参数。提议的内嵌限制移动最小平方的算法,通过在幽灵图像点附近对所有内部节点应用移动最小平方的计算法,并在相应的边界条件中对这些内部节点的相关镜面图像点应用一个移动最小平方的计算法,最大限度地减少了在幽灵点图像点图像点处的内插偏差。使用分析模型,ECMLS算法与有限的移动最小平方的算法(CMLS)算法以及使用各种网格大小、内插基功能、重量函数和约束度的罚法参数值值差差差。发现,在所调查的传播应用中,使用ECMLS的移动平面、立面和双基基基计算结果也比平面模型模型的平流率值要好,在内部平面上,在使用最低平面平面的递测线基础中,在使用最低的里程的里程轨道函数,在最优的里程范围内的里程中,以显示的里程的里程的里程的里程计算。