Numerical Studies On The THINC Method For Trimmed Meshes With Applications For Interface Capturing In Water Wave Problems

The free interfacial flows of water waves are commonly existed in the area of ship building and ocean engineering.When designing the marine structure or analyzing the flow mechanism,the related interfacial flows need to be simulated.In recent years,the simulation method based on the CFD(computational fluid dynamics)technique is widely used,where both the mesh type and the interface solving method have important impacts on the computational accuracy and efficiency.When the computational domain is very complex,the unstructured mesh is usually selected for the spatial discretization.Presently,the trimmed mesh is very commonly applied,since it can be efficiently refined and has good orthogonality and adaptability properties.Meanwhile,the VOF(volume of fluid)method has become one of the most widely used interface-capturing methods,due to the significant advantage of mass conservation.Particularly,the VOF scheme can be separated into three types,including the geometric,algebraic,and hybrid geometric/algebraic types.At present,the interface is mainly captured by the algebraic VOF schemes on trimmed meshes.In general,the algebraic VOF schemes are relatively simple and can be suitable for arbitrary cell topologies,but the accuracies are relatively low with the higher numerical diffusion.Although the geometric VOF schemes are usually very accurate,their implementations are very complex,especially for the unstructured mesh.In recent years,the unstructured THINC schemes,which belong to hybrid geometric/algebraic VOF schemes,can obtain comparable accuracies to the geometric VOF schemes,without explicitly geometrical interface reconstructions.However,there are many complex cell shapes in the trimmed mesh,which are beyond the application range of some efficient unstructured THINC schemes.Besides,the face splitting and the existence of hanging vertices would interfere with the judgement for the cell and face types.In such cases,the existing unstructured THINC schemes cannot be applied for the trimmed meshes,so a series of extension and application studies were made by this paper.Firstly,the THINC schemes were extended for the main cell types of the trimmed meshes.The key point is to reconstruct the interface only based on the main feature of the split-face unstructured cell,but the real cell topologies are considered when calculating the VOF fluxes.Particularly,THINC/QQ(THINC method with quadratic surface representation and Gaussian quadrature)and UMTHINC(unstructured multidimensional THINC)schemes were extended,forming the so-called THINC/QQ-SF(THINC/QQ extended for split-face unstructured cells)and UMTHINC-SF(UMTHINC extended for split-face unstructured cells)schemes,respectively.Meanwhile,a series of standard VOF advection cases were carried out to systematically validate the extended THINC schemes,based on the trimmed meshes designed by this paper.Additionally,the algebraic scheme of HRIC(high-resolution interface capturing)and the geometric high-accuracy scheme of isoAdvector,were also involved for comparisons.These results indicate that THINC/QQ-SF has superiorities when the accuracy,interface compactness,and efficiency are simultaneously concerned.Secondly,this paper has played an important role in developing the in-house mulit-phase CFD solver,i.e.UMCFD(unstructured mesh computational fluid dynamics),based on which the real water waves were solved.In the simulations of gravity collapse of stratified fluids and dambreak,the collocated PISO(pressure implicit with splitting of operators)algorithms were compared between the total pressure form and the modified pressure form,indicating that the two forms have no significant differences when simulating small density-ratio flows,but the latter form is more suitable for large density-ratio flows.For the gravity collapse of stratified fluids,physical experiment validations were also conducted,based on the newly designed experimental device.Besides,THINC/QQ-SF can well capture the large deformation and breaking of the wave surface,and has advantages over HRIC both in maintaining the interface compactness and in predicting the impact pressure force.To be noted,HRIC also has good properties before the wave surface has violent deformations.Finally,the application strategies of THINC/QQ-SF were studied for real engineering problems.The hybrid method with HRIC,called THINC/QQ-SF&HRIC,was proposed based on the cell distribution characteristics of complex trimmed meshes.And HRIC was only used to deal with the complex polyhedral cells,whose quantity and space ratios are very small.By using sub-cycles within each time step,the hybrid VOF method can be suitable for large CFL numbers to explicitly solve the VOF advection equation,with stable performances.In the simulations of induced wave and resistance for the surface vessel DTMB(David Taylor model basin)5415,the hybrid VOF method could obtain similar results by using fewer(or much fewer)mesh cells,compared with the VOF type references.Especially,THINC/QQ-SF which is the key interface capturing scheme,could effectively suppress the unphysical mixture between water and air,both on the high-speed hull surface and on the wave breaking regions,so that the reliability of numerical prediction is increased.Both the application strategies and the performance analyses,are important explorations for the unstructured THINC schemes to be used in complex engineering problems.