A Cut-cell-based Sharp-interface Method For Fluid-Structure Interactions

Fluid-structure interactions(FSIs)exist in many scientific and engineering problems.It is a interdisciplinary field that involving fluid mechanics,solid me-chanics,numerical mathematics and so on.It is very important to address the material interface accurately and stably in numerical studies of FSI problems.In this work,a new integrated,conservative and consistent cut-cell-based sharp-interface method is developed by including a strong-coupling fluid-structure interaction for linearly elastic solids and elastic-perfectly plastic solids based on the sharp-interface method for compressible multi-phase flows(Chang,Deng&Theofanous,J.Comput.Phys.,2013)to simulate compressible multi-material problems with various interfaces in 2D situation.In the current method,dif-ferent fluid-fluid,fluid-solid and solid-solid interfaces are treat,ed in a uniform framework,in which the material interfaces are represented by quadratic-curve cut faces evolved with the help of the level set equation.Multiple level set func-tions are applied to address multiple interfaces.For t,he int,eraction between linearly elastic solids,the adoption of finite vol-ume method ensure that this method is fully conservative.In this work,the exact linearly elastic Riemann solver developed by Kaboudian and Khoo(Kaboudian&Khoo,J.Comput.Phys.,2014)in Lagrangian framework is achieved in Eu-lerian framework,which is used to calculate the numerical flux on the cut faces to achieve the strong coupling at the interface.Comparisons among the exact solution,cut cell method and different ghost solid methods show current method gives accurate wave front location,and is stable for high density and acoustic impedance ratio and high order reconstruction.The solid in the FSI problem is normally elastic and plasticizes when it is beyond the von Mises yield criterion,which may occur under a strong impact or large deformation.The exact,Riemann solver for 'stiffened-gas' EOS based elastic-perfectly plastic material developed by Gao and Liu(Gao and Liu,Adv.Appl.Math.Mech.2017)is employed to calculate the numerical flux.This Riemann solver includes six different wave structures:elastic shock wave,elas-tic rarefaction wave,plastic shock wave,plastic rarefaction wave,elastic-plastic shock wave and elastic-plastic rarefaction wave.One-dimensional numerical tests show that the current method successfully decrease the non-physical oscillations near the material interface and is more accurate and more stable than the MGFM used for comparison.In 2-D aluminum rod impacting an aluminum target case,current method can express the evolution of the interface clearly.2-D underwater explosion case shows the ability,accuracy,stability and convergence of the cur-rent method,additionally,it shows that with the different,constitutive equations,different compressibilities will lead to different results.Synthesizes all the Riemann solvers for fluid.linear clastic and elastic-perfectly plastic materials,we can get a multi-phase Riemann solver,different Riemann solvers are applied on the regular faces and cut faces under same-fluid,two-fluid,fluid-solid and solid-solid situations and the interfacial velocitias are obtained from these Riemann solutions.The system is mainly developed in Eulerian coor-dinates with the cut faces moving in a Lagrangian manner;thus,it benefits from a Lagrangian moving interface in terms of accuracy and handles large deforma-tions more conveniently than those works in a Lagrangian framework.Coupling these two framework in FSI problems is one of the future work.