An approach for numerically solving nonlinear diffusion equations on 2D scattered point distributions is developed with finite directional difference method. The approach yields stencils of minimal size using five neighboring points. And coefficients of discretization have explicit expressions. A scheme employing five-point formulae is proposed to discretize multimedia interface condition for discontinuous problems in which approximation to flux on interface is second-order accurate. The discretization methods show good performance in numerical examples with different computational domains and different point distributions.

To investigate mechanism of TUDOG(transeverse uniform singlet oxygen generator),a chemical reaction model is made to describe physical and chemical performances of Cl₂/He mixed gases transversely traveling into a falling BHP(KOH,H₂O₂,H₂O)drop field.Numerical computation is carried out.In two-phase flows,exchange of mass and momentum between two phases is considered.One set of 2-D gas-phase flow equations are solved with SIMPLEC scheme.Simulation results agree well with experiments provided in references.It is found that chlorine utility and singlet oxygen yield decreases with increase of gaseous inflow speed,and increases with speed of falling drops.Absorb and utility of chlorine mainly takes place in reactive region upstream.

A Lagrangian finite point method for two-dimensional compressible hydrodynamics problems is presented.The numerical scheme is based on scattered points inside a computational domain without need for a specific connectivity.A cloud of five neighbors is selected around each point at each time step,and this cloud is used to implement finite point schemes based on five-point approximation formulas to gather information about flow derivatives.For numerical stability concerns,four artificial Laplace operators are introduced and added to corresponding conservative equations,respectively.Furthermore,an adaptive strategy for time step is also provided.Numerical results show validity and potential interest on this approach.

A Lagrangian finite point method for one-dimensional compressible multifluids is presented.The proposed method is a meshfree numerical procedure based on a combination of interior point scheme and interface point tracking algorithm.The discretization of unknown function and its derivatives are defined only by position of the so called Lagrangian points.The interior point formulation is based on Taylor series expansion in continuous regions on both sides of a interface.Unlike most current meshfree method,a point is settled at the interface position initially.State of interface point is updated using Rankine-Hugoniot conditions at interface together with characteristics difference computation.The interface tracking algorithm is the main feature of the method.Numerical tests show that the algorithm is oscillation-free at material interfaces and accuracy of the method is demonstrated.