Research And Application Of TVD Limiter Scheme Based On Cut-Cell Method

The multiphase flow involving moving objects is a hot issue in the study of hydrodynamics of ships and marine engineering in recent years.Cartesian grids method based on non-boundary-fitting system have advantages over boundary-fitting system for multi-bodies with any complex shape.The cut cell finite volume method under Cartesian grid system not only retains the advantages of the Cartesian grid,but also has conserved properties,which is very suitable for multiphase flow with moving bodies.However,at the interface between the gas and liquid field,there is surface tension and the physical density jumps greatly,which lead to discontinuity of pressure and viscous stress or sharp gradient solution.The traditional linear high-order convection schemes usually generate non-physical oscillations near the discontinuity or large gradient solution.Therefore,it is necessary to apply nonlinear high-resolution schemes,among which the TVD flux limiter approach has been widely used and applicable to regular grids.Thus,the TVD limiter approach is studied and applied to the cut cell method within this paper,in order to suppress the non-physical oscillations near the discontinuity or large gradient solution.The main content of this paper is summarized as follows:Chapter 1 describes the advantages of Cartesian cut cell finite volume method for nonlinear two-phase flow with multi-bodies,and highlights the significance of the high-resolution TVD limiter method in numerically solving such problems.Then the paper review the current situations of the TVD limiter approach,including its property and applications under different CFD grid systems.Three kinds of turbulence models are analyzed for multiphase flow problems,among which the LES(Large Eddy Simulation)shows great advantage.Chapter 2 analyze the discretization and flux solution of convection terms,the finite volume solution and gradient reconstruction in the cut cell method are also presented.Secondly,the TVD limiter method are compared with other high-resolution schemes.The principle,expression construction and constraint conditions of TVD limiter method are elaborated in detail.In addition,the slope limiters are transformed into flux limiters.The characteristics of TVD constraint region of flux limiters are described and the connection and difference between the TVD and NVD systems are also analyzed.Classification and the properties of the flux limiter functions in TVD and NVD frameworks are performed.Finally,the dimension-splitting scalar limiter algorithm for multidimensional problems are described,along with the finite volume limiter algorithm for equation systems and numerical waves based on feature splitting.Chapter 3 introduces the large eddy simulation platform developed by our laboratory.The principle and characteristics of the multi-body mass force model are introduced,as well as the solution process of the implicit finite volume algorithm based on cut cell methods.The focus is based on the high resolution TVD limiter method under the cut cell framework.In Chapter 4,based on the large eddy simulation solver of our laboratory,the paper combines the mass force model and the cut-cell TVD limiter approach to simulate the case of water entering problem,and compares the results of the flux limiter method with the experiment,verifying effectiveness of the limiter approach for cut cell method.In summary,this paper applied TVD flux limiter approach to cut cell method,basing on finite volume Navier-Stokes solver with multi-body mass force model and regular control volumes.The approach is aimed to achieve high accuracy and strong stability by adaptively adjusting velocity gradient.It is different from the slope limiter method in gradient reconstruction process,with formulation unrelated to the cutting sizes.The approach works by modifying the anti-diffusion flux,and is simple in algorithm,easy to implement and can ensure diagonally-dominant property for discrete equations.