Development Of Acceleration Computational Techniques For Meshless Particle MPS Method And Their Applications

Moving particle semi-implicit(MPS)method is one of meshless particle methods for truly imcompressible fluid.The fluid is represented by a set of computational points(or particles).Due to its Lagrangian and meshless nature,MPS is quite suitable to deal with flows involving large free surface deformation and/or moving boundaries.However,the traditional MPS is proposed based on the uniform mass particle distribution in the entire domain.When the local flow field needs to be refined,one has to discretize the entire domain by fine particles.This may lead to computational cost increasing sharply.Therefore,it is significant to develop a local refine technique in the frame of MPS method.Based on the improved MPS method,Zhang developed a meshless particle solver MLParticle-SJTU 1.0 which has been applied into numerous free surface flows.However,the entire computational domain should be represented by single resolution particles in the solver.In the present work,the Overlapping module and Multi-resolution module are developed based on the particle solver MLParticle-SJTU.Furthermore,the solver MLParticle-SJTU 1.0 is also upgraded to new version MLParticle-SJTU 2.0.The Overlapping module is developed based on the overlapping particle technique and the improved MPS(IMPS)adopted in the particle solver MLParticle-SJTU 1.0.The overlapping particle is one technique to refine local flow field in the context of MPS method.The main idea of this technique can be summarised as follows: firstly,give a local concerned region or overlapping region.Then,distribute the low-resolution particles in the entire domain and the high-resolution particles in the overlapping region.In each one loop time step,the flow field by low-resolution particles is solved firstly to obtain the entire flow field and provide the truncation boundary information for recalculating the flow field in the overlapping region by high-resolution particles.Since no high-resolution particles are distributed outside the overlapping region,high-resolution particles need to be generated and deleted dynamically.When the fluid flows in the overlapping region,high-resolution particles should be generated.When the fluid flows out the overlapping region,the corresponding high-resolution particles should be deleted.In this paper,an algorithm to generate the fine particles is carried out based on the coved area or volume of an imaginary cell by coarse particles.Furthermore,the flow chart of OPT is simiar to that using the uniform mass particles in the entire domain.Overlapping module in the MLParticle-SJTU 2.0 solver is applied into the large deformation free surface flows,including wave breaking problem,2D dam breaking and 3D dam breaking with obstacle.In the first case,the shoaling,breaking and post-breaking of a solitary wave on a slope plane is performed to validate the present overlapping particle technique.The numerical results show that OPT can depict the fine free surface deformation with less CPU computational time.In 3D dam breaking case,water front impacts the obstacle and then changes its direction of motion and forms a jet.The comparison of the numerical results between uniform resolution technique and overlapping particle technique shows that OPT can reproduce the same accurate shape of free surface as that using fine particles in the entire domain.In addition,jet particles by universally coarse(Uni-Coarse)seem much scattered than that by OPT and universally fine(Uni-Fine).The evolutions of the impact pressure by three numerical simulations are also illustrated.Pressure peak by OPT is close to that by Uni-Fine,but greater than that by Uni-Coarse.Furthermore,the CPU time by OPT is about half of that by Uni-Fine.Multi-resolution particle technique is also a local refine technique in the MPS.Different from the overlapping particle technique,different resolution particles are distriubted in the entire domain directly in the multi-resolution technique and a strong coupling strategy between different size particles is employed.All different resolution particles are coupled together to resolve the pressure Poisson equation(PPE).For two different size particles,the influence domain of coarse particle contains the fine particle but not vice versa.The radii of supported domain for two different size particles are replaced by their arithmetic values.In addition,the modification for pressure gradient model is deduced based on the force continuity between two neighboring particles.Furthermore,the Multi-resolution module is develped,where the Multi-resolution particle technique is embedded into our in-house solver MLParticle-SJTU 1.0.The multi-resolution particle technique is applied to the dam breaking problems.Firstly,the multi-resolution technique is applied to 2D dam breaking problem.The recorded pressure shows that multi-resolution technique can provide the overall tendency of pressure with that by Uni-Fine.Then,a 2D dam breaking with obstacle is performed by uniform resolution technique and multi-resolution particle technique,respectively.Morever,the multi-resolution particle technique is applied to 3D dam breaking problem.The multi-resolution particle technique is further applied to water entry problems.Firslty,both half and neutral buoyant circular cylinder entering water are carried out by multi-resolution particle technique and uniform resolution particle technique respectively.In the case using multi-resolution technique,the zone close to the impact area is distributed with finest particles and one far from the impact area is represented by coarsest particles.The numerical results show that the particle distributions in both Uni-Fine and Multi-MPS are much more integrated than that in the Uni-Coarse,where the behaviors of free surface movement in the former two cases are quite similar.Furthermore,liquid splashing can be observed obviously in the former two cases,but is not clear in the Uni-Coarse case.Then,the neutral buoyant cylinder case is extended to 3D one.In addition,water entry of a cylinder with an initial angle is also carried out by the multi-resolution technique and the overset grid technique in grid-based solver naoe-FOAM-SJTU,which can further verify the reliability of the multi-resolution technique.Finally,effects of initial impact speeds of cylinder are investigated.In the present work,two particle refine modules are developed based on our in-house code MLParticle-SJTU 1.0,and the code is also upgraded to new version MLParticle-SJTU 2.0.The main purpose of these two modules is to reduce the necessary particles and further decrease the computational load caused by refining the entire domain.Generally speaking,overlapping particle technique and multi-resolution particle technique can be considered as indirect acceleration computation techniques in the MPS method.