Study On The Mathematical Model Of Sediment Wave Move Based On SPH And Couette Flow Method

Submarine sand wave movement is an important part of the study on the flow sediment removal and deposition law theory,and also one of the engineering research questions on the evolution of riverbed,seabed scouring and sediment bed.As the social economy grows,urban construction in inland and coastal areas has brought river control and ocean resources utilization to the government's schedule.Sediment on riverbed or seabed can affect,either slightly or heavily,shipping,water intake projects,river regulation,etc.Therefore,the study of sand wave movement has great social significance.In-depth scientific research has been carried out around sediment wave motion,and the following research results have been achieved:(1)It introduces the rationale and governing equation of meshless SPH method,and conducts detailed analysis through establishment of numerical modeling by SPH method.In the research process,the impact by surface tension was considered through free surface particle search technology;the preliminary impact effectbetween droplet and liquid level was solved through artificial viscosity technology;the treatment boundary conditions of boundary virtual particle and mirror virtual particle were introduced in,so that the boundary defects of particle method can be better solved and that the instability of real particles in the corner of the vessel can be eliminated.Using the SPH method to simulate the droplet impacting on liquid surface,which shows the SPH method is better than other methods.It introduces basic ideas and basic equations of DEM.The repose angle of two dimensional and three dimensional about sediment accumulation in air or water can be simulated by using coupling model of SPH-DEM,which can reflect the characteristics of sediment accumulation.(2)Proceeding from N-S equations,the define solution problem of vorticity function,fluctuating velocity and pulsating pressure functions in shear flow were established by adopting the Oseen transformation and fluctuating velocity features.It proposed the circulatory integral solution for the first time and attained the velocity,speed and pressure solutions of vertical turbulence along the wall surface;in the analysis of relations among major parameters,a research approach is provided to vortex theory study and its practical engineering application.The Airy equation solution in special function theory to complex function field was expanded.It conducted research on the complex planar solution of Airy function by means of circulatory integral,and thus obtained vorticity function,fluctuating velocity and pressure functions'analytical solutions to vertical linear gradient distributed flow,which also provides a new thought for theory research.Thefunction form of third derivatives was offered and the expression of equation solution was simplified.Based on boundary conditions,it conducted qualitative research on the distribution trend of vorticity and pressure function in the linear gradient distributed flow,and analyzed the stability of the movement trail of particles.The expression of theory approximate solution was offered,and also was compared it with previous researchers'test results after choosing parameters;thus it proves that the theory approximate solution can describe the variation trend of the test data,which provides a new method for the research of same-type engineering problems.(3)Starting from characteristic line theory and based on the thought of shock wave discontinuous solution,the approximate Rieman solution was introduced,which is based on Roe scheme,so as to calculate the numerical flux in the unit interface.It adopts TVD-MUSCL and Hancock schemes to improve the space and time precision of the calculation model to stage two,and thus establishes a two-dimension unsteady hydro-dynamic model equipped with stage-two time and space precision;as a result,the time and space precisions of the model is improved.A wet-dry boundary technology was adopted to satisfy the stability of calculation and ensure the conservation of water yield in the calculation.Through proof calculation of classic calculating examples,it proves the model has a comparatively high computational accuracy and good stability,and that the model is able to dispose various complex flow states,including slow flow,rushing flow,as well as the combination of both.Thus,the basic flow computational simulation conditions of the model are provided.(4)Couette flow was used to express the bottom flow,and SPH method was used to express the sediment bed surface,the interaction force of particles,which is not only consideredthe influence range ofthe kernel function,but also applied connection mode of particle contact force(DEM).The sediment layer in the open channel is loaded with smoothed particles;Couette laminar flow forms the bottom flow between particles and the open channel flow;the shear force of the Couette flow works on boundaries of smoothes particles,to lead particles on the bed surface to enter a motion state or recover the state of rest.For the channel sediment mathematical model,a layered coupling method was adopted,which is contained three layers—the upper layer,middle layer and the under layer.Firstly,the upper-layer model works out the flow;secondly,to work out the Couette shear stress on the boundary of smoothed particle bed and Couette flow's upper edge;at last,to work out the deformation of the particle bed by setting the shear stress as the boundary condition of the smoothed particle bed,so as to correct the water depth of the upper-layer model.It also illustrates the feasibility of establishing models in the complete cyclic process.The changing process is well fitted.(5)The feasibility of the model's simulation of the occurrence of waves was explained,by adopting a channel water sediment numerical model to simulate the occurrence of sand ripples.It describes the motion morphology of sand waves;the speed of the sand waves is basically accord with the empirical formula and with previous researchers'test results;it also analyzes and establishes the mathematic model simulating sand wave movement.It conducts a research on the moving rules of sand ridges and sand waves by setting engineering sand waves as an example,providing basis to design and construction of submarine pipeline roads.The calculated sediment content and the measured sediment content are at the same level;the calculated variable quantities and measured variable quantities of the sand ridges and waves are in the same tendency.The model can basically reflects the physical variation process of the primary form,and can be used to simulate variations of original-shape sand ridges and waves,as well as to forecast the moving rules of sand ridges and waves.