Research On Fluid Calculation Using Numerical Manifold Method Based On Independent Covers

It is an important problem in engineering design to study the damage of surging wave to the safety of hydraulic structures caused by landslide in reservoir bank.It is of great practical significance to study the numerical simulation method of surging wave.In this paper,the key problem of the numerical simulation of surging waves fluid is to solve the Navier-Stokes equation(hereinafter referred to as N-S equation)with free surface,and a new numerical calculation method,the Numerical Manifold Method based on independent covers,is used for research.The main works are as follows:(1)Study the one-dimensional convection-diffusion problem.The field variables of such flow problems are prone to sudden increase or decrease within a small spatial scale.The existing numerical calculation methods may have unreasonable numerical oscillation,numerical dissipation and other calculation stability and calculation accuracy problems when solving such problems.In order to solve these problems,sufficient segmentation of the solution domain,such as a uniform mesh for the entire solution domain,will increase a large amount of computation,so adaptive solution has important significance.Aiming at the above problems,the new idea of Numerical Method for solving one-dimensional convection-diffusion equation analysis based on independent covers is proposed,which is the approximation using polynomial series piecewise-defined.Firstly,The solution formula of the one-dimensional convection-diffusion equation is derived based on the standard Galerkin method;secondly,The posterior error estimation method about the continuity of the first-order derivative of the field variable in the narrow overlapping area between independent covers is used for the automatic solving by h-p hybrid self-adaptive analysis with mesh refinement and ascending series order.Finally,two classic examples are selected for analysis.The results show that: the numerical solution of the piecewise-defined series and the exact solution fit well.For the convection dominated problem,the adaptive solution can effectively avoid numerical oscillation and so on,and has higher computing accuracy with less computing resources.In addition,the error index of the residual by substituting thenumerical result back to the differential equation is successfully attempted.This is the most stringent errorjudgment for the numerical solution so far.(2)Study the one-dimensional Burgers equation,which is the basis of the two-dimensional N-S equation,including the nonlinear convection term and the diffusion term,but not the pressure gradient term,which has a certain representative.The Burgers equation contains a nonlinear convection term,which brings a lot of inconvenience to the numerical calculation.Therefore,the semi-Lagrangian idea is introduced,and the series solution of the previous step is used to find the position of the fluid particle of the current step at the previous step,and its velocity is used as the initial speed of the current step.Thereby eliminating the convection term and the nonlinearity it brings,greatly reduces the difficulty of the solution and improves the efficiency of the solution.First,The solution formula of the one-dimensional Burgers equation is derived,including the conventional format(Euler method)and the semi-Lagrangian format;then two initial boundary value problems are selected for adaptive solution and compared the calculation accuracy and efficiency of the two formats.The results show that the semi-Lagrangian method has higher calculation efficiency under the condition of ensuring the calculation accuracy;for the shock wave example,the adaptive solution can accurately identify the position of the shock wave and describe the shock wave with high accuracy come out.(3)Study the two-dimensional incompressible N-S equation.First,the calculation formula of the two-dimensional N-S equation is derived,including the steady-state equation and the transient equation,and the transient equation includes Euler format and semi-Lagrangian format;The drive flow of the square cavity top cover is solved,and the numerical results are very consistent with the classical literature solution,including the semi-Lagrangian format;finally,the error index of the residual by substituting thenumerical result back to the differential equation is also successfully attempted.(4)In the transient analysis of the two-dimensional incompressible N-S equation,the semi-Lagrangian method was used to preliminarily study the tracking problem of the free surface of fluid movement,which is in good agreement with the calculation results of commercial software.In summary,this paper uses the Numerical Manifold Method based on independent covers to conduct preliminary research on the fluid flow problems related to surge,design and implement the Numerical Manifold Method based on independent covers to solve these fluid flow problems,and verify the vadility and reliability of the new method in fluid calculation through numerical examples,which lays a good foundation for simulating the surge and its impact on hydraulic structures.The Numerical Manifold Method based on independent covers used in this paper is expected to provide a high-precision,high-efficiency numerical tool for computational fluid dynamics.