Study on Development and Applications of Moving-Grid Fininte-Volume Method
In this paper, the Moving-Grid Finite-Volume Method (MGFVM) has been developed and has been applied to various flow problems. The MGFVM is the numerical method suitable for simulations of an unsteady flow driven by moving boundary, such as a body moving in a fluid. The MGFVM is a finite-volume method constructed based on a four-dimensional control-volume in the space and time unified domain (x, y, z, t); therefore, the method satisfies automatically both geometric conservation laws (GCL) and physical conservation laws simultaneously. Three kinds of developments of the MGFVM have been performed in this paper. Firstly, the MGFVM has been extended to unstructured grid system. For compressible flows, it has been developed on both structured grid system and unstructured grid system. For incompressible flows, however, it has been developed on only structured grid system. Thus, in this paper, the detailed formulation of the MGFVM for incompressible flows on unstructured grid system has been described and it has been validated using test problems. Secondly, the MGFVM has been applied to the simulation of fluid-body interaction. As is well known, “Digital Flight” is a recent grand challenge in the research field of computational fluid dynamics. In this paper, as a one of the approaches to the Digital Flight, the simulation procedure of fluid-body interaction using the MGFVM is presented. The MGFVM for fluid-flow solver, the Forward-Euler finite-difference scheme for body-motion solver and the Quaternion for representation of body-rotation are combined in order to solve the system of the fluid-body interaction in the procedure. The approach has been applied to a floating motion of “Fukidama”, a flying motion of “Boomerang”, a fall motion of “Parachute” and a swimming motion of “Jelly-fish”. The results have shown excellent agreement with experimental data. Finally, in order to refine a resolution of flow solutions at discontinuity existing in flow field, a “Neural network” approach has been combined with the MGFVM. The neural network is a system of programs that simulates the operation of the human brain. In this paper, an adaptive mesh refinement has been implemented using the information of the flow discontinuities such as shock wave detected by the neural network of spatiotemporal visual processing. The results have shown good improvement of the resolution at the discontinuities.