Simulation Methods And Statistical Analysis For Simplified Stochastic Hyperbolic Conservation Laws

As an interdisciplinary subject,statistical computing covers a wide range of fields such as statistics,computational mathematics,computational science,etc.It mainly uses computational methods and statistical software as tools for numerical simulation and analysis of models to solve practical problems.In this thesis,a simplified model of the stochastic conservation laws is studied,the corresponding numerical method is used to prepare the program and plot the simulation,and the data obtained from the simulation is statistically analysed to predict a reasonable and effective simulation method.First,this thesis aims to find an effective numerical simulation method for a simplified model of the stochastic conservation laws.In order to overcome the difficulty that the flux is discontinuous across the stationary discontinuity,which results in the jump of the unknown function,the Godunov-type numerical flux is written in the positive and negative fluxes for the first time and embedded between two discontinuous flux functions.With the Godunov flux-splitting,an ideal numerical method(MDFLU-WENO5)is proposed through the essentially non-oscillatory reconstruction of the flux and the thirdorder Runge-Kutta time discretization method with variation diminishing,which has good effect at discontinuity.Secondly,based on Godunov-type numerical flux splitting,we use the upwind method and THINC(Hyperbolic Tangent)function to obtain the upwind numerical fluxes of positive and negative fluxes at cell boundaries.Then,we adopt the corresponding downwind template to obtain the downwind numerical fluxes at cell boundaries for both the positive and negative fluxes.The final upwind numerical flux is determined for the positive and negative flux respectively through the two-stage boundary variation diminishing principle to minimize the jumps of the reconstructed values at the cell boundaries(denoted as P4T2-BVD),which can effectively control numerical oscillation and dissipation.The system of equations is analyzed in the above proposed method,which further verifies the feasibility and effectiveness of the simulation method.Finally,through programming calculations and numerical experiments,using curve regression in statistical calculation methods,SPSS statistical analysis is performed for simulated data,and it is found that the first simulation method proposed(MDFLUWENO5)has the advantages of simplicity,good balance and no oscillation.In addition,statistical analysis can predict that the P4T2-BVD method has better advantages than the MDFLU-WENO5 method,which provides a direction for further study of the simulation method for the simplified model of the stochastic conservation laws.