Methane and air premixed combustion around a cylinder is chosen to evaluate reduced mechanisms of 16species/41steps, 15species/19steps and 53spesies/325steps. The coming flows are homogeneous. Turbulence and its interaction with combustion, fuel diffusion are neglected and finite reaction rates of chemistry are assumed in the computation. The 5th order WENO scheme that conserves free flow properties is used to mitigate derivative errors from unsmooth grids and increase solution accuracy. Pressure and temperature contours as well as their distributions along stagnation line are obtained including mass fractions of species CH₄, CO and CO₂. Bow shock and flame front both appear upstream the cylinder. Standoff distances and induction lengths are related to reduced mechanisms. With increasing cylindrical diameter, standoff distances increase and induction length decrease either for ignition delay. The bow shock and flame are both pushed upstream but they are still remained in sequence. In contrast to reduced models of 16species/41steps and 15species/19steps, 53spesies/325steps model provides good accuracy and ignition covers a wide range of pressure and temperature. Three models demonstrate incompletely burning or chemical reactions in all cases except cases of cylinders with large diameters. It shows that elementary reactions reach chemically equilibrium but the reactions are not so completely. Meanwhile, the larger cylindrical diameter, the better accuracy in evaluation of reduced chemistry mechanisms.

Flow field induced by a moving shock interacted with cylindrical water columns and a nozzle flow field was numerically investigated. Fixed Cartesian grids are used and level-set method combined with revised real ghost fluid method (rGFM) is applied for tracking gas-water and gas-solid interfaces. Fifth order WENO schemes are employed for solving Eulerian and level-set equations as well as reinitialization equations. Nozzle contours are simplified as gas-solid interface, and nozzle contour profiles are expressed by splines for ease of obtaining normal vector. In the case of shock interacting with water columns, schlieren images and pressure time histories at specified points are shown to describe shock evolution and mitigation downstream. It indicates that complex shock structures are distinguished accurately by the method, and shock transmission and reflection occur on gas-water interfaces of neighboring columns in a row and in a column respectively. In addition, pressure, density contours and velocity of nozzle flow field is in agreement with inviscid solution by gas dynamics theory, which demonstrates effectiveness and robustness of level-set method coupling with rGFM for computing flow field in a complex geometry involving gas-water and gas-solid interfaces.

To obtain second order accuracy in SPH scheme, sufficient conditions for smooth functions are discussed and formula are presented. Uniqueness is analyzed for solution of the second order particle approximation. SPH approximate solutions are numerically validated to arrive at nearly second accuracy in the case of periodic boundary conditions. While particle number increases, L₁-error decreases and L₁-order approaches to the second order particle approximation of SPH scheme.

A moving planar shock interacting with multi-material interfaces in compressible fluid on fixed Descartes grids is studied. Level-set method combined with a revised real ghost fluid method(rGFM) are applied for tracking gas-water and gas-solid interfaces, where a revised Riemann problem is constructed and its approximate solutions are populated for real and ghost fluid status. WENO schemes are employed for Euler and level-set equations. Numerical schlieren images are obtained for demonstrating shock evolution. Complex shock structures distinguish accurately and show various interfaces embedded in the fluid. Other than partition and coordinate transformation, we offer an approach for computation of complex flow field on Descartes grids involving multi-material interfaces or objects.

To study truncation of an integral function and unphysical penetration of particles near an interface, treatment of boundary conditions at a gas-liquid interface was proposed based on concept of ghost fluid method(GFM). Ghost particles are copied into kernel domain for avoiding truncation of integral function. Parameters are specified near interface for ghost particles according to density distribution method. Drags produced by slip velocity between particles of gas and liquid are included in computation. With comparison of results obtained by methods of SPH and level-set on shock wave interacting with a gas-liquid interface, acceptable numerical precision is shown since results are basically identical for calibration examples. Results are both obtained for cases of streaming around an initially fixed water cylinder and a fall-off of a water cylinder. The phenomena seem physically resasonable based on obtained results. Treatment of gas-liquid interface boundary condition approximately avoids truncation of an integral functions near interface and prevents numerical oscillation, particles penetration for SPH methodology. Pressure and normal velocity are kept continuously on both sides of gas-liquid interface during computation.

With concepts of virtual particles, we present a method for inlet and outlet boundary conditions. Inlet zone is located just outside inlet boundary, which is defined and filled with virtual particles. Outlet and buffer zones are located just outside outlet boundary. Quantities of outlet boundary virtual particles are calculated, and quantities of buffer boundary virtual particles are imposed. According to stream status of every time step, zone property of fluid particles could to be changed. Relevant fluid particles are added or remored, when boundary virtual particles inflow or outflow fluid domain. With SPH method based on N-S equation, two-dimensional pipe flow is used to verify boundary conditions. Finally boundary conditions applied in calculation models of shock tube and flow around a cylinder are studied. Inlet and outlet boundary conditions are proposed to avoid fluid particles integral truncation near border, and to assure fluid particles and shock wave flow out boundary.