Improved Meshfree Riemann-SPH Method And Its Applications

Many fluid flows exist in the field of ship and ocean engineering,such as underwater explosion,hydrodynamic slamming on structures and so on.These phenomena are related to some difficult fluid problems such as large deformation of fluid,fluid-solid coupling effect and nonlinear evolution of multiphase materials.As a widely used meshless particle method,smooth particle hydrodynamics(SPH)method has inherent Lagrangian advantages in dealing with fluid splash,large deformation of free surface and multiphase moving interface problems.Since this method was put forward in the last century,SPH method has been applied in the fields of free surface flows,multiphase flows,compressible flows and fluid-structure interactions,and it has obtained fruitful research achievements.At present,based on the conventional SPH,many improved versions have been developed,such as δ-SPH and RiemannSPH.However,compared with mature grid methods.SPH method still has many limitations.such as poor numerical accuracy,pressure instability and low calculation efficiency.These shortcomings limit the application of SPH in some problems,such as high-precision simulation of complex flows and simulation of flows involving strong discontinuities.In order to remedy the above shortcomings,this thesis attempts to enhance the ability of SPH method under the framework of Riemann-SPH.A Riemann-SPH single-phase model with low dissipation property,a multiphase Riemann-SPH model for water-air flow with high density ratios,an elastomer solver based on the Riemann-SPH method,a fluid-structure interaction model based on the Riemann-SPH,a Riemann-SPH shock-capturing scheme for strong discontinuity problems and a high-order Riemann-SPH scheme based on TENO reconstruction are established.With the help of the numerical model established above,the numerical simulation of free surface flows,slamming of structures into the water,fluid-solid coupling considering elastic responses,multiphase flows with high density ratios,high Reynolds number flows,compressible flows with strong discontinuities,compressible flows with rich fluid details have been realized.Firstly,this thesis introduces the basic theory of the conventional SPH method.On this basis,an interacting particle pair in SPH are constructed into a one-dimensional Riemann problem,and then the Riemann-SPH scheme is established by introducing this problem into the governing equations.In this scheme,Roe’s approximate Riemann solver is applied to solve the Riemann problem.Compared with the traditional SPH method,the hidden dissipation of the Riemann-SPH method is separated,and then we find the similarity between the Riemann-SPH method and the δ-SPH method by comparing with the δ-SPH method.In order to improve the computational efficiency of the SPH method,on the basis of conventional linked-list search algorithm,an adaptive linked-list search algorithm is developed.For the coupling problems between the object and the free surface flows,a single-phase model based on the Riemann-SPH with low dissipation property is proposed.In this model,a dissipation limiter is designed to reasonably control the implicit dissipation in the momentum equation.An equivalent relation between the dissipation term in the dissipation limiter and the Reynolds number is derived.Based on the elastic mechanics,the Riemann-SPH method is applied to the elastic structure simulation,and an elastic structure solver without artificial parameters is proposed.The accuracy is verified by several benchmark examples.Results show that the proposed structure solver overcomes oscillations caused by traditional model using artificial viscous force.Then,we coupled the Riemann SPH fluid solver with this structure solver,proposing a unified fluid-solid coupling numerical model.Through the numerical simulation of hydroelasticity problems,the calculation accuracy and numerical stability of the model are verified.For the water-air flows,we regarded the two-phase interface as a contact discontinuity problem,and then with the advantage of Riemann SPH in dealing with discontinuity problems,we proposed a Riemann-SPH multiphase model to solve water-air flows with large density ratios.Roe’s Riemann solver combined with the designed dissipation limiter can reproduce the two-phase interface,and obtain smooth and continuous pressure fields at the interface.With respect to the water-air problems,different from the traditional multiphase SPH model,the present model can consider the real sound speed and the real compressibility of air.In addition,compared with the traditional SPH method,this model can use a larger time step,thus improving the computational efficiency when handling multiphase flows.The proposed multiphase Riemann-SPH model can reproduce multiphase flows with complex interfaces,flows with different Reynolds numbers,multiphase flows with high density ratios,and slamming of structures into the water with satisfactory accuracy.With respect to the compressible flow problems with shock waves,a new shock-wave capturing scheme based on the Riemann SPH method is proposed.In this scheme,a new dissipation limiter is designed,which can effectively adjust the numerical dissipation in the continuity equation,and considering the kernel function gradient correction technique,the numerical accuracy of the strongly compressible flow problem is improved.This scheme is a numerical method without any adjustment parameters and there is no need to use adjustable artificial viscosity in this scheme.More importantly,we can replace the equal mass particle distribution with the equal spacing particle distribution,which greatly simplifies the initial particle setup process.Through the simulation of compressible flow problems with strong discontinuities,it is found that the scheme has good numerical accuracy and excellent numerical stability.It can capture sharp shock profiles and reproduce many small-scale flow structures.For the problem of low numerical accuracy of the SPH method,in the framework of Riemann-SPH,a TENO reconstruction technique in mesh-based method is applied to the left and right states of the Riemann problem,and then a high-order TENO-SPH scheme is proposed.The convergence tests prove that TENO reconstruction can significantly improve the accuracy of the SPH method.In order to successfully apply the TENO reconstruction technique to the SPH method,for the five equal spacing stencil points required in the TENO method,we regarded two interacting particles as the existing two stencil points,and then we find the particle closest to the missing stencil point in the direction of particle pair.Through the gradient approximation,we can obtain the primitive values of these three missing points.After finding the appropriate stencil points,the TENO reconstruction technique for the primitive variables is deduced,and finally,the high-order reconstruction of the left and right states of the Riemann problem is achieved.TENO-SPH method can be applied to many fluid dynamics problems,including typical compressible flows and incompressible flows,which contributes a new numerical scheme to the SPH community.