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compact finite difference-FOURIER SPECTRAL METHOD FOR THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

Acta Mechanica Sinica 1996年第4期12卷 296-306页

作者：熊忠民凌国灿 LNM Institute of MechanicsChinese Academy of SciencesBeijing 100080China

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

关键词： compact finite difference Fourier spectral method numerical simulation vortex dislocation

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A compact Eulerian Interface-Capturing Algorithm for Compressible Multimaterial Elastic-Plastic Flows with Mie-Gr uneisen Equation of State

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Advances in Applied Mathematics and Mechanics 2023年第2期15卷 485-521页

作者： Xiang Li Dong-Jun Ma Nan-Sheng Liu Pei Wang Institute of Applied Physics and Computational Mathematics Beijing 100094China Department of Modern Mechanics University of Science and Technology of ChinaHefeiAnhui 230027China Center for Applied Physics and Technology Peking UniversityBeijing 100871China

This paper presents an Eulerian diffuse-interface method using a high-order compact difference scheme for simulating elastic-plastic flows with the Mie–Gruneisen(MG)equation of state(EoS).For simulations of multimaterial problems,numerical errors were generated in the material discontinuities owing to inconsistent treatment of the convective *** on the normal-stress-based mechanical equilibrium assumption for elastic-plastic solids,we introduce an improved form of the consistent localized artificial diffusivity(LAD)method to ensure an oscillation-free interface for velocity and normal *** proposed algorithm uses a hyperelastic model.A mixture type of the model system was formed by combining the conservation equations for the basic conserved variables,an equation of a unified deviatoric tensor describing solid deformation,and an additional set of equations for solving the material quantities in the MG *** one-and two-dimensional problems with various discontinuities,including the elastic-plastic Richtmyer–Meshkov instability,were considered for testing the proposed method.

关键词： Multimaterial elastic-plastic flow Eulerian solid-dynamics high-order accurate schemes compact finite difference localized artificial diffusivity

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Fast High Order Algorithm for Three-Dimensional Helmholtz Equation Involving Impedance Boundary Condition with Large Wave Numbers

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American Journal of Computational Mathematics 2023年第2期13卷 211-229页

作者： Chengjie Tong Xianqi Fang Meiling Zhao School of Mathematics and Physics North China Electric Power University Baoding China

Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.

关键词： Impedance Boundary Condition Helmholtz Equation compact finite difference Fourier Sine Transform Large Wave Numbers

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INTERACTIVE STUDY BETWEEN IDENTICAL COHERENT STRUCTURES IN THE WALL REGION OF A TURBULENT BOUNDARY LAYER

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Journal of Hydrodynamics 2002年第1期14卷 100-105页

作者： Lu Chang-gen (College of water Resources and Environment, Hohai University, Nan jing 210098, China) College of water Resources and Environment Hohai University Nanjing 210098 China

A theoretical model for identica l coherent structures in the wall region of a turbulent boundary layer was propo sed, using the idea of general resonant triad of the hydrodynamic stability. The evolution of the structures in the wall region of a turbulent boundary layer wa s studied by combining the compact finite differences of high numerical accuracy and the Fourier spectral hybrid method for solving the three dimensional Navier -Stokes equations. In this method, the third order mixed explicit-implicit sch eme was applied for the time integration. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, an d the sixth-order center compact schemes for the derivatives in spectral space were introduced, respectively. The fourth-order compact schemes satisfied by th e velocities and pressure in spectral space was derived. As an application, the method was implemented to the wall region of a turbulent boundary to study the e volution of identical coherent structures. It is found that the numerical result s are satisfactory.

关键词： coherent structure turbulent bounda ry layer compact finite difference

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Explicit High-Order Method to Solve Coupled Nonlinear Schrödinger Equations

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Advances in Pure Mathematics 2021年第5期11卷 472-482页

作者： Khadijah Alamoudi Mohmmad Said Hammoudeh Department of Math King Abdulaziz University Jeddah Saudi Arabia

Models of the coupled nonlinear Schrödinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refraction. In this article, we will presuppose the compact finite difference method with Runge-Kutta of order 4 (explicit) method, which is sixth-order and fourth-order in space and time respectively, to solve coupled nonlinear Schrödinger equations. Many methods used to solve coupled nonlinear Schrödinger equations are second order in time and need to use extra-technique to rise up to fourth-order as Richardson Extrapolation technique. The scheme obtained is immediately fourth-order in one step. This approach is a conditionally stable method. The conserved quantities and the exact single soliton solution indicate the competence and accuracy of the article’s suggestion schemes. Furthermore, the article discusses the two solitons interaction dynamics.

关键词： Coupled Nonlinear Schrodinger Equations Sixth Order Method Interaction of Two Solitons compact finite difference Runge-Kutta of Order 4 Method

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