Discontinuous Galerkin Finite Element Numerical Simulation And Its Application In Digital Core

As an new and developing numerical simulation method,the discontinuous galerkin finite element method inherited the merits of the traditional finite element numerical simulation method.The grid processing is flexible,and can solve the complex geological structure problem with undulating surface and drastic change of parameters.Moreover,it has the discontinuous characteristics that the traditional finite element method does not have,and it has the natural parallelism.At the same time,the selection of the basis function is flexible,which can easily improve the accuracy of forward simulation.Therefore,in this thesis,the discontinuous galerkin finite element seismic wave field simulation method and its application in the digital core is studied.Based on the elastic wave equation,the governing equations of discontinuous galerkin finite element method are derived,and the mass matrix,stiffness matrix and boundary flux are given.Then Runge-Kutta time discrete schemes are combined to iterate.For the boundary reflection problem,the absorbing boundary conditions and the nearly perfect matching layer are adopted.The simulation results indicate that these boundary conditions can effectively absorb false reflections at the artificial boundary.In addition,the parallel MPI method is used to accelerate the computational efficiency of forward simulation.In order to verify the practicability of the discontinuous galerkin finite element numerical simulation method.Firstly,the numerical solution is compared with the analytical solution in the uniform medium model and the layered medium model to verify the reliability of the method.Then,the method is extended to the complex undulate surface model,which prove that the method is applicable in complex models.Finally,it is applied to the dynamic simulation of digital core elastic parameters.The calculation of elastic parameters based on digital cores has always been a key problem in the field of rock physics,but real rocks are usually highly heterogeneous,and conventional numerical simulation methods are easy to cause numerical instability,the discontinuous characteristic of discontinuous galerkin finite element method make it easy to adapt to the heterogeneity of rock.In this paper,the discontinuous finite element method based on unstructured triangular meshes is used to simulate the propagation process of elastic wave in digital core samples,and the equivalent elastic modulus is calculated according to the ultrasonic measurement experiment.The simulation results based on carbonate samples show that the elastic modulus calculated by discontinuous galerkin finite element method is within the limit of H-S and Voigt,which proves the practicability of the method.