FSI modeling with the DSD/SST method for the fluid and finite difference method for the structure

SummaryThe fractional step method (FSM) is an efficient solution technique for the particle finite element method, a Lagrangian‐based approach to simulate fluid–structure interaction (FSI). Despite various refinements, the applicability of the FSM has been limited to low viscosity flow and FSI simulations with a small number of equations along the fluid–structure interface. To overcome these limitations, while incorporating nonlinear response in the structural domain, an FSM that unifies structural and fluid response in the discrete governing equations is developed using the quasi‐incompressible formulation. With this approach, fluid and structural particles do not need to be treated separately, and both domains are unified in the same system of equations. Thus, the equations along the fluid–structure interface do not need to be segregated from the fluid and structural domains. Numerical examples compare the unified FSM with the non‐unified FSM and show that the computational cost of the proposed method overcomes the slow convergence of the non‐unified FSM for high values of viscosity. As opposed to the non‐unified FSM, the number of iterations required for convergence with the unified FSM becomes independent of viscosity and time step, and the simulation run time does not depend on the size of the FSI interface. Copyright © 2016 John Wiley & Sons, Ltd.

Investigation on the delayed closure of the suction valve in the refrigerator compressor by FSI modeling

In this paper, a special integrable negative-order Calogero–Bogoyavlenskii–Schiff equation (nCBS) in fluid mechanics is studied by means of the symmetry reduction method and consistent tanh expansion method. The Painlevé integrability is investigated to confirm the compatibility conditions. This integrable nCBS equation has been transformed into different reduction equations and the corresponding invariant solutions with arbitrary functions are obtained. The corresponding structures of the invariant solutions for the nCBS equation are also shown graphically. At last, new types of soliton–cnoidal interaction solutions for the nCBS equation are presented through the consistent tanh expansion method on the basis of the truncated Painlevé expansion.

The flow of fuel inside the high-pressure fuel tube is the basis of many fuel-engine operations. The regulation of the internal pressure of the high-pressure fuel tube is a key factor affecting the efficiency and stability of the fuel engine. Therefore, the research on this subject has important industrial significance. This article first introduces the specific working principle of a high-pressure fuel system, and analyzes the factors affecting the internal pressure of the fuel tube. Then the Bernoulli equation and continuity equation in fluid mechanics are introduced, and the actual ejection rate change at the nozzle is obtained. Finally, a finite difference method was used to establish a simulation model for high-pressure tube operation. Then a high-pressure tube pressure regulation system was constructed, and the relationship between the cam speed and the pressure control in the high-pressure tube was explored with simulation.

Summary Based on molecular mechanics, a new structural mechanics model, a 2-D frame composed of equivalent anisotropic beams and flexible connections, is proposed for the simulation of the static and dynamic flexural behavior of monolayer graphene. The equivalent beam representing the C-C bond in the new molecular structural mechanics (MSM) model has two salient features compared with other MSM models proposed for the analysis of carbon nanotubes: one is that the flexible connections at the beam ends are used to account for the bond-angle variations between the C-C bonds; and the other is that there are two principal bending rigidities used, respectively, for the in-plane bending energy associated with bond angle variations and the inversion energy to characterize the different behaviors of the i?3-bond and i??-bond in the graphene lattice. The mechanical properties of the equivalent beam representing the C-C bond in the graphene lattice are evaluated from the molecular mechanics. The in-plane mechanical properties as well static and vibrational flexural behaviors of monolayer graphene are analyzed using the proposed new MSM model coupled with ANSYS. The simulation results show that the 2-D flexibly connected frame model of the new MSM model proposed in this paper gives improved predictions of the in-plane Young’s moduli, Poisson ratios and flexural rigidities of monolayer graphene than other MSM models. The present study also indicates that the modeling of bond angle variation is very important in the mechanical behavior simulations of graphene lattice. For example, the present new MSM model in which a monolayer graphene is modeled as flexibly connected planar lattice predicts very good results of Poisson ratios of graphene, but on the other hand the original MSM model in which a monolayer graphene is modeled as rigidly connected planar lattice yields much smaller Poisson ratios although this structural mechanics model is able to predict a quite good longitudinal deformation, The present study also shows that monolayer graphene sheet is kind of an anisotropic material since both the in-plane elastic properties and the flexural rigidities of monolayer graphene are chirality dependent.

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.

Finite-difference (FD) schemes have been used widely for solving wave equations in seismic exploration. However, the conventional FD schemes hardly guarantee high accuracy at both small and large wavenumbers. In this paper, we propose an optimal time-space domain FD scheme for acoustic vertical transversely isotropic (VTI) wave modeling. The optimal FD coefficients for the second-order spatial derivatives are derived by approaching the time-space domain dispersion relation of acoustic VTI wave equations with the combination of the Taylor-series expansion and the sampling interpolation. We perform numerical dispersion analyses and acoustic VTI modeling using the optimal time-space domain FD scheme. The numerical dispersion analyses show that the optimal FD scheme has smaller dispersion than the conventional FD scheme at large wavenumbers, and also preserves high accuracy at small wavenumbers. The acoustic VTI modeling examples also demonstrate that the optimal time-space domain FD scheme has greater accuracy compared with the conventional time-space domain FD scheme for the same modeling parameters.

A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction

A quantative comparison between the boundary integral equation (BIE) method and the finite difference (FD) method is presented in which each technique is applied to an elliptic boundary‐value problem (BVP) containing a boundary singularity. Two types of singularity have previously been analysed theoretically, namely those due to a discontinuous boundary potential, which we shall refer to as S1, and those due to a sudden change from the specification of boundary potential flux, an S2 singularity. In this paper the analysis is presented for a third type of boundary singularity, namely an S3 singularity: that arising from a discontinuous boundary flux. Such a condition is frequently encountered in the field of heat transfer where, for example, a system or pipe has a change of lagging material.In general, it is found that the BIE method is superior, with regards to the computational time required to achieve a certain degree of accuracy, over standard FD methods even when there is a boundary singularity. Further, the BIE method determines the solution near the singularity much more accurately than the FD method. The FD method does, however, have advantages for a very restrictive class of problems; for example, when the boundary conditions are of the Dirichlet type and the boundary geometry is rectangular. In this case an optimum relaxation parameter can easily be obtained. A soon as Neumann conditions are prescribed, the BIE is far more efficient than the FD, whatever the boundary geometry.It is concluded that, for fast, accurate solutions of general Laplacian boundary‐value problems, the BIE is appreciably superior to the FD and this is even more pronounced when there is a boundary singularity.

3D MRI-based multicomponent thin layer structure only plaque models for atherosclerotic plaques

Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev–Petviashvili equation in fluid mechanics

A CFD-FEM based partitioned fluid structure interaction model to investigate surface cracks in elastohydrodynamic lubricated line contacts

A finite element method (FEM) for solution of the conservative full potential flow equation is presented as a means for improving the computation of transonic flows about complex geometries. The method does not require an orthogonal mesh, thus removing a major constraint in grid generation. A standard Galerkin finite element formulation is used in conjunction with the artificial compressibility method which stabilizes the algorithm in transonic flow and allows the capture of embedded shock waves. Solution comparisons, including one test case which stresses the'capabilities of state-of-the-art finite difference methods, verify the FEM accuracy and geometric capability. I. Introduction W HILE the computation of inviscid two- and threedimensional flowfields by finite difference methods has now become commonplace in industry, one of the most important technological deficiencies is in the area of geometric modeling, particularly for transonic flows. The finite element method (FEM) is presented as a way of alleviating some problems of geometric modeling which limit the effectiveness of current finite difference methods. Certain specific advantages of the FEM, if fully exploited, may improve greatly the computational state-of-the-art. Since the governing equations of inviscid transonic potential flow are nonlinear, the method of superposition (i.e., panel methods) is insufficient to yield a proper solution, even though solutions have been obtained by a method combining surface singularities and field differences.1 Also, because of the nonlinearity, similarity laws do not exist which allow subsonic flows to be related to transonic flows. Field methods must be used, typically finite difference or finite element methods, requiring a grid of points to be defined, both on the body surface arid in the flowfield, on which solutions to the governing equations are approximated. Finite difference method (FDM) computer codes generally

Body-fitted and Cartesian grid methods are two typical types of numerical approaches used for modelling fluid–structure interaction problems. Despite their extensive applications, there is a lack of comparing the performance of these two types of approaches. In order to do this, the present paper presents benchmark numerical solutions for two two-dimensional fluid–structure interaction problems: flow-induced vibration of a highly flexible plate in an axial flow and a pitching flexible plate. The solutions are obtained by using two partitioned fluid–structure interaction methods including the deforming-spatial-domain/stabilized space–time fluid–structure interaction solver and the immersed boundary–lattice Boltzmann method. The deforming-spatial-domain/stabilized space–time fluid–structure interaction solver employs the body-fitted-grid deforming-spatial-domain/stabilized space–time method for the fluid motions and the finite-difference method for the structure vibrations. A new mesh update strategy is developed to prevent severe mesh distortion in cases where the boundary does not oscillate periodically or needs a long time to establish a periodic motion. The immersed boundary–lattice Boltzmann method uses lattice Boltzmann method as fluid solver and the same finite-difference method as structure solver. In addition, immersed boundary method is used in the immersed boundary–lattice Boltzmann solver to handle the fluid–structure interaction coupling. Results for the characteristic force coefficients, tail position, plate deformation pattern and the vorticity fields are presented and discussed. The present results will be useful for evaluating the performance and accuracy of existing and new numerical methodologies for fluid–structure interaction.

Comparison of Eulerian and Lagrangian numerical techniques for the Stokes equations in the presence of strongly varying viscosity