DSMC Method On Unstructured Grids For Hypersonic Rarefied Gas Flow And Its Parallelization

Hypersonic vehicles encounter a broad range of flight conditions varying from continuum to rarefied flows. In rarefied regime, the molecular effects are important and the assumptions of continuum methods become invalid. Due to the facts that the available ground tunnel experimental techniques and test facilities are limited and attempts to solve the Boltzmann equation have met with many difficulties, the Direct Simulation Monte Carlo (DSMC), originally developed by Bird in 1960's, has become a widely used computational tool for the rarefied gas flows. The purpose of the present thesis is to study detailed DSMC method on unstructured grids for hypersonic rarefied gas flows and to develop highly efficient automated DSMC software that is suitable for any complex geometry.First of all, necessary basic molecular kinetic theory of gases is studied for DSMC. Binary elastic collision is analyzed in detail and the expression of post collision velocities is deduced. Intermolecular potential and different collision model is discussed. Based on some existing results, a new molecular collision model for DSMC, called GSS-3 model, is introduced to provide consistency for the transport properties with Lennard-Jones potentials that is a realistic intermolecular potential.Secondly, the implementation of DSMC method on unstructured grids is investigated to calculate hypersonic rarefied flow. The idea of sub-cell in Bird's Position Element Method is introduced into the DSMC method on unstructured grids, by which only ID number of sub-cell is stored. An automatic searching method is presented to improve efficiency and save running time, which is a coupling of area/volume coordinate searching technique and alternative digital tree (ADT) searching algorithm. As a consequence, not only is the computation time reduced, but also the precision is improved largely. The deterministic criterion for a molecule to reflect on a certain surface element is used by ADT algorithm instead of a probabilistic one. Extensive numerical experiments are made to directly simulate hypersonic rarefied gas flows.Then, based on the work of implementation of DSMC method on unstructured grids, this thesis is to study strategies for optimization and improvement of key technique in DSMC method on unstructured grids. A new automatic searching algorithm is presented by calculating intersection point, by which all information about molecules hitting surface boundary can be given and the deterministic criterion is used for a molecule to reflect on a certain surface element instead of a probabilistic one as used in position element method. In order to improve efficiency and save running time, an adaptive local time stepping suitable for DSMC method on unstructured grids is designed. Collision distance is introduced to DSMC method on unstructured grids which can avoid bad errors due to large scale dimension of some unstructured grids. A new data structure based on unstructured grids is introduced to achieve high performance and efficiency. Accessing molecular data is direct other than traditional data structure that is indirect by cross-reference array. Dynamic allocation feature of Fortran90 is fully exploited, which makes the code more flexible. By comparisons of efficiencies of numerical experiments, the feasibility of the method is confirmed.Afterwards, DSMC method on unstructured grids is studied to calculate rarefied gas flows with chemical reactions. The collision theory for chemical reactions is discussed and the probability function of reaction (or steric factor) of different collision models is deduced for direct simulation of chemical gas flow. A subroutine is incorporated into existing DSMC code on unstructured grids in order to simulate chemical reaction rarefied gas flow.At last, this thesis is to investigate parallel algorithm of DSMC method on unstructur- ed grids using the MPI standard library on PC-CLUSTER that is distributed memory architecture. In order to obtain high parallel performance, a new adaptive domain decomposition technique is presented. Because this method results in equal number of molecules among processors, dynamic load balance is maintained. Two different communication methods are constructed by means of MPI library: single step communication and multiple step communication method. A complete parallel implementation of DSMC method on unstructured grids included 2D and 3D is developed using SPMD and master/slave parallel mode. This new tool is applied to numerical experiments, which are used to evaluate the performance of parallel DSMC code on unstructured grids.