Numerical Computing Methods For Some Direct And Inverse Problem Of High Dimensional Thermo-Fluid Coupling Equations

The thermo-fluid coupled problem is widespread in the development and utilization of geothermal resources,radioactive waste disposal,natural gas development,groundwater exploitation and so on.In this paper,the coupling model of high dimensional heat flow is analyzed,and the difference scheme of the coupling equation is deduced.The numerical equations of the obtained discrete equations are numerically analyzed,and the parameters of the coupling model are solved numerically.In this paper,several thermo-fluid coupled models are analyzed,and the governing equations of a Thermo-fluid coupled model are discussed in detail.The finite difference scheme of coupling equations with the alternating direction iteration(ADI)method and the truncation error and stability are analyzed,and the conditional stability of the difference scheme is obtained.The nonlinear equations can be obtained by the direct dispersion of the heat flow coupling equation.Because of the nonlinear equations are difficult to solve,we first obtain the numerical solution of the seepage velocity at the discrete point of the steady-state seepage equation,and replace the discrete heat conduction equation to convert the nonlinear system into a linear system.In the case of high dimension,the spatial domain and the time domain grid are discretized and the nodes are too many,which leads to the large order of the discrete equations.The linear order of the coefficients of the system is large.The linear equations are solved by Thomas algorithm and Crout decomposition.In order to improve the calculation accuracy,the generalized minimal residual(GMRES)algorithm is used to solve the problem,and the convergence of the iterative method is discussed.The numerical simulation is carried out to verify the feasibility of the numerical method.In this paper,the inverse problem of the parameters of the thermo-fluid coupledequation is discussed.The numerical scheme of the parameter inversion of the two-dimensional thermo-fluid coupled equation is given.The inversion scheme of the parameter is analyzed and simulated with the simulated annealing algorithm.