Lattice-Boltzmann Simulation For Fluid Flow And Real-Time Visualization

In this dissertation, we study the computer simulation and visualization of complex system. The main research topics comprise complex flows and complex terrain.Fluid flow is one of the most important fields to the national economy and the people's livelihood. The study direction of flow comprises scientific computing and visualization. Being a mesoscopic method that uses simple microscopic models to simulate macroscopic behavior of transport phenomena, the Lattice-Boltzmann Method(LBM or LB) has many unique advantages, such as easy implementation, good locality and natural parallelism, and has developed into a useful tool for simulating complex flows and modeling complicated physics phenomena. In this dissertation, based on the mathematics evolutionary method, we have systematically studied the efficient algorithms for simulating complex flows and the real-time flow visualization techniques in the aspect of theory, the design of algorithms, implementations and applications.Firstly, some results of the lattice Boltzmann method are introduced, including an incompressible LB model without compressible effect, a flexible thermal LBM with simple structure for Boussinesq fluids, and a robust boundary scheme. We use them to simulate the lid-driven cavity flow at Reynolds numbers 5000 ~50000, the natural convection due to internal heat generation in a square cavity at Rayleigh number up to 10 12, respectively. The numerical results agree well with those of previous studies.Secondly, a unified lattice BGK (ILBGK) model iDdQq for the incompressible Navier-Stokes equation is presented. To test its efficiency, the lid-driven cavity flow in three-dimensional space for Reynolds number Re =3200 and span aspect ratio SAR =1,2and 3 is simulated in detail on 48×48×(48×SAR) uniform lattice using the model. The test results agree well with those in previous experiments and numerical works and show the efficiency and strong numerical stability of the proposed ILBGK model.Thirdly, a unified thermal LBGK model for the Boussinesq incompressible fluids is introduced. In the model, the velocity and temperature fields are solved by two independent LBGK equations which are combined into a coupled one for the whole system. Numerical simulations of three-dimensional natural convection flow in rectangular enclosures with differentially heated vertical walls are performed at Rayleigh numbers 1 .5×103 ~7.5×104and Prandtl numbers 0 .015and 0 .025. The numerical results are compared with those of a previous study.And fourthly, a software system of visualization with real-time show of the computing results is developed in terms of the evolutionary characteristics of the LBM. The system supports the real-time display for the scale or vector field results which are obtained in the process of LBM evolutionary computation, the tracing show of result in the special position, the reset of the computing parameters in real-time, the preservation of the results and play them in motion picture as well as the show of 2D or 3D results. It provides a convenient and efficient research platform to the theoretical study and practical applications of LBM. Compared with the traditional visualization software, this software has its special characteristics on flow computation and the idea of software design.Digital Earth is another important area of visualization and has got a wide application. The digitizing of terrain information is a foundational work for us to construct Digital Earth. In this dissertation, we have developed a great deal of efficient algorithms and software technology to solve the difficult problem of vectorizing the scanned topographical maps which are mountainous and filled of complex terrain. We present a lot of fast recognition algorithms of contour lines from scanned topographical maps and a thinning algorithm of contour lines based on the contour vectors which are recognized; a real-time recognition and vectorizing software based on the algorithms is developed. By using this software, 166 complicated scanned topographic maps of the Qingjiang basin with ratio 1:10000 and an area of 4000 square kilometers had been successfully vectorized. It shows that the algorithm is a fast, accurate and highly effective one.