Analysis And Application Of Energy Reduction Algorithm For Sharp-interface Two-phase Flow Model

This research focuses on the energy decay algorithm for direct numerical simulation based on the FTM(Front Tracking Method)in two-phase flow.It is divided into two major parts: the study of the energy decay algorithm of integer-order two-phase flow model,and the study of the energy decay algorithm of fractional-order two-phase flow model.The study of the energy decay algorithm of integer-order two-phase flow model.In theory,for the integer-order two-phase flow model,it is proved to satisfy the energy inequality for the continuous compressible and incompressible problems.Then,we propose the fully explicit discretization scheme of the two-phase flow problem which uses a combination of the finite difference method for the space approximation and the first-order forward time schemes.We prove that the proposed numerical scheme fulfills a discrete version of the energy inequality for both compressible and incompressible systems.The algorithms for sharp-interface modeling is totally energy-decay.In numerical simulation,A front-tracking method is developed for direct numerical simulation of the model.The interface is tracked by marker points and they are connected.Interfacial source terms like surface tension are computed on the front and transferred to the fixed grid.The density is used to be the indicator function and reconstructed at the location of front.The results show that: it is very good agreement with the actual physical laws which verify the efficiency of the proposed numerical methods.The study of the energy decay algorithm of fractional-order two-phase flow model.Based on the integer-order two-phase flow model,it is generalized and a fractional-order two-phase flow model is established using fractional theory.In theory,the key of our model is that the first-order time derivative of the standard Navier-Stokes equation is replaced by a Caputo fractional derivative,which makes the problem become global in time.This model is proved to satisfy the energy inequality.We present a computationally effective explicit difference approximation to solve the time fractional derivative.Then,we propose a fully explicit discretization for the fractional Navier-Stokes equations which uses a combination of the finite difference method and the first-order forward time schemes.Also,the proposed numerical scheme is proved fulfills a discrete version of the energy inequality.The algorithms for fractional two-phase modeling is totally energy-decay.In numerical simulation,A front-tracking method is developed for direct numerical simulation of the model.It is same as the method used in integer-order twophase flow model.The simulation results for different fractional derivatives are shown and compared.In this paper,in short,these studies have great significance for further study of the two-phase flow energy decay algorithm.