An Implicit Multicloud Convergence Accelerator for Compressible Flows

In this study, we developed an implicit multicloud method using geometric conservative meshless discretization. The Geometric Conservation Least Squares Method (GC-LSM) was used for meshless discretization which allowed lower–upper symmetric Gauss–Seidel (LU-SGS) time integration to be implemented in a multicloud context. The LU-SGS algorithm for meshless discretization was implemented in the same framework as the unstructured finite volume method owing to the properties of the GC-LSM. The developed method was tested for three-dimensional inviscid flows on unstructured grids. The explicit 4th-order Runge–Kutta method and the implicit LU-SGS algorithm were compared to demonstrate the effect of the proposed implicit multicloud method. Furthermore, the restriction functions were modified for three-dimensional space. The results highlight the capability of the implicit multicloud method combined with the original multicloud coarsening procedure, which is straightforward and mesh-transparent, by only applying GC-LSM for discretization.