Nonlinear Dynamic Fluid-Structure Interaction Calculations With Coupled Finite Element and Finite Volume Programs

In this paper a robust and effective 4–node shell element for the structural analysis of thin structures is described. A Hu–Washizu functional with independent displacements, stress resultants and shell strains is the variational basis of the formulation. With application of three basic assumptions within the FE formulation a stabilized one point integrated element comes out automatically. Besides static computations it can be used for dynamic problems with explicit or implicit time integration without further adaptions. The element possesses the correct rank and fulfills the membrane and bending patch test. The stabilization terms can be integrated analytically and do not require an input of problem dependent control parameters. In contrast to several approaches the results are not path dependent for hyperelastic material behavior. This unphysical behavior follows when the material matrix of the last load increment is used in the stabilization matrix to preserve quadratic convergence in the Newton-Raphson iteration. The element possesses the well-known robustness of Hu–Washizu elements with the possibility of very large load steps in nonlinear applications. Another essential advantage of present development is the application to FE2 computations where the computing times are dominated by the solution of the micro problems at the shell integration points. Depending on the used interpolation for the shell strains the new element is approximately by a factor 4 or 9 faster than the corresponding version with full integration.

SummaryTo improve the computational efficiency of the numerical manifold method for discontinuous deformation simulations, a spatial‐domain coupled explicit‐implicit time integration algorithm is proposed. A subdomain partition algorithm based on a super manifold element is developed for the numerical manifold method to simulate dynamic motions of blocky rock mass. In different subdomains, explicit or implicit time integration method is employed respectively based on its contact and motion status. These subdomains interact through assembling the corresponding explicit or implicit time integration‐based matrices of different rock blocks. The computational efficiency of the discontinuity system under dynamic loading is improved by partially diagonalizing the global matrices. Two verification examples of a sliding block along an inclined plane under a horizontal acceleration excitation and a multiblock system acted on by dynamic forces are studied to examine the accuracy of the proposed numerical method, respectively. A highly fractured rock mass situated on an inclined slope subjected to seismic excitations is then studied to show the computational efficiency of the developed algorithm. The simulated results are in good agreement with those from the versions using purely implicit or explicit time integration algorithm for the numerical manifold method. The computational efficiency is shown to be higher using the proposed algorithm, which demonstrates its potential for application in dynamic analysis of highly fractured rock masses.

A coupled implicit-explicit time integration method for compressible unsteady flows

Implicit–explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning

This survey paper reviews some recent developments in the design ofrobust solution methods for the Navier--Stokes equationsmodelling incompressible fluid flow. There are twobuilding blocks in our solution strategy. First, an implicit time integrator that usesa stabilized trapezoid rule with an explicitAdams--Bashforth method for error control, and second, arobust Krylov subspace solver for the spatially discretized system.Numerical experiments are presented that illustrate the effectivenessof our generic approach. It is further shown that the basic solution strategy can bereadily extended to more complicated models, includingunsteady flow problems with coupled physics and steady flow problems thatare nondeterministic in the sense that they have uncertain input data.

Stabilization of the Lax-Wendroff method and a generalized one-step Runge-Kutta method for hyperbolic initial-value problems

This work presents the development of an explicit/implicit particle finite element method (PFEM) for the 2D modeling of metal cutting processes. The purpose is to study the efficiency of implicit and explicit time integration schemes in terms of precision, accuracy and computing time. The formulation for implicit and explicit time marching schemes is developed, and a detailed study on the explicit solution steps is presented. The PFEM remeshing procedures for insertion and removal of particles have been improved to model the multiple scales of time and/or space of the solution. The detection and treatment of the rigid tool contact are presented for both, implicit and explicit schemes. The performance of explicit/implicit integration is studied with a set of different two-dimensional orthogonal cutting tests of AISI 4340 steel at cutting speeds ranging from 1 m/s up to 30 m/s. It was shown that if the correct selection of the time integration scheme is made, the computing time can decrease up to 40 times. It allows us to affirm that the computing time of the PFEM simulations can be excessive due to the used time marching scheme independently of the meshing process. As a practical result, a set of recommendations to select the time integration schemes for a given cutting speed are given. This is intended to minimize one of the negative constraints pointed out by the industry when using metal cutting simulators.

This research conducts a comparative study of finite element analysis (FEA) in tube hydroforming (THF). The investigated tube is stainless steel grade 304 (SS304) of as received and after annealing (AN). Three different finite element modeling techniques have been examined and compared with corresponding experimental results. The main modeling parameters of interest range from element technologies, symmetry modeling, and solving schemes. Other parameters being sensitive to each model are discussed. Formability issues have been investigated through FEA and forming limit diagram (FLD). Computational aspects have been illustrated and discussed for simulating THF and an intermediate AN. Prediction of the required forming pressure is challenging. Both shell and continuum elements have different advantages and drawbacks in simulating THF. A shell element with explicit time integration tends to underpredict the required forming pressure while both axisymmetric and 3D continuum elements with implicit time integration tend to overpredict the required forming pressure. The draw-in observation can also provide an insight of the state of deformation.

This article develops high‐order implicit time‐stepping methods combined with the fourth‐order central essentially‐non‐oscillatory (CENO) scheme for stiff three‐dimensional computational fluid dynamics problems having disparate characteristic time scales. Both aerodynamic and magnetohydrodynamic problems are considered on three‐dimensional multiblock body‐fitted grids with hexahedral cells. Several implicit time integration methods of third‐ and fourth‐order accuracy are considered, including the multistep backward differentiation formulas (BDF4), multistage explicitly singly diagonally implicit Runge‐Kutta (ESDIRK4), and Rosenbrock‐type methods (ROS34POW2). The resulting nonlinear algebraic system of equations is solved via a preconditioned Jacobian‐free inexact Newton–Krylov method with additive Schwarz preconditioning using block‐based incomplete LU decomposition. The performance of the high‐order implicit time‐stepping methods on smooth and stiff problems is compared with a standard fourth‐order explicit Runge‐Kutta (RK4) method. It is shown that the Rosenbrock methods, despite their advantage of only requiring the solution of linear systems, have significant drawbacks in terms of robustness issues for highly nonlinear compressible flows. The implicit BDF4 and ESDIRK4 methods are found to be much more efficient than the explicit fourth‐order RK4 method for a stiff resistive magnetohydrodynamic (MHD) problem discretized with the fourth‐order CENO method. When applied to the problem of vortex shedding governed by the Navier–Stokes equations, an A‐stable ESDIRK4 scheme proved to be the more robust and accurate implicit time‐marching scheme and was able to offer significant speedup compared with the RK4 method. Initial results are also shown for high‐order implicit time integration applied to two problems with discontinuities. The current study represents the first to achieve high‐order implicit time integration for MHD, enabling large time steps and substantial speedups for stiff MHD problems with high‐order accuracy, and it also represents the first to establish high‐order implicit time integration for high‐order CENO in space.

We simulate sand dynamics using an elastoplastic, continuum assumption. We demonstrate that the Drucker-Prager plastic flow model combined with a Hencky-strain-based hyperelasticity accurately recreates a wide range of visual sand phenomena with moderate computational expense. We use the Material Point Method (MPM) to discretize the governing equations for its natural treatment of contact, topological change and history dependent constitutive relations. The Drucker-Prager model naturally represents the frictional relation between shear and normal stresses through a yield stress criterion. We develop a stress projection algorithm used for enforcing this condition with a non-associative flow rule that works naturally with both implicit and explicit time integration. We demonstrate the efficacy of our approach on examples undergoing large deformation, collisions and topological changes necessary for producing modern visual effects.

A modified method has been suggested to improve the computational efficiency of a multiresolution analysis for implicit temporal integrations. The fundamental idea behind multiresolution analysis is that high cost computations such as flux evaluation are performed only at the cells where the salient flow features exist, thereby reducing the computational cost. The multiresolution analysis, however, suffers from numerical inefficiency in implicit time integration because the efficiency of the multiresolution analysis method arises mainly from a reduction in the expensive flux evaluation for spatial discretization. This paper demonstrates that the implicit temporal integration of multiresolution analysis can be substantially improved by reducing the implicit operator matrix to the size of the additional residual dataset. To suppress the numerical error from the reduced implicit operation, the operator matrix is derived based on the additional residual dataset constructed by the decomposition and thresholding of the residuals, and the thresholding criterion is modified to retain the numerical accuracy at a high Courant–Friedrichs–Lewy number. The accuracy and efficiency of the present modified multiresolution analysis are verified through various application flow problems, such as a stationary vortex, a steady airfoil, an airfoil vortex interaction, and a transonic wing, ranging from two-dimensional steady/unsteady to three-dimensional steady applications. The results show that the computing speed of the modified multiresolution analysis with lower–upper symmetric Gauss–Seidel is about twice as fast as that of a baseline computational fluid dynamics solver on steady and unsteady simulations, while maintaining the accuracy of the solver.

This study investigates the full penetration simulation of piles from the ground surface, focusing on frictional contact modeling without mesh distortion. To overcome issues related to mesh distortion and improve solution convergence, the Arbitrary Lagrangian–Eulerian (ALE) adaptive mesh technique was implemented within both explicit and implicit time integration schemes. The numerical model was validated against field experiments conducted at Bothkennar, Scotland, using the Imperial College instrumented displacement pile (ICP) in soft clay, where the soil behavior was effectively represented using the modified Cam-Clay model and the Mohr–Coulomb model. The primary objectives of this study are to evaluate the ALE method performance in handling mesh distortion; analyze the effects of soil–pile interface friction, pile dimensions, and various dilation angles on pile resistance; and compare the effectiveness of explicit and implicit time integration schemes in terms of stability, computational efficiency, and solution accuracy. The ALE method effectively modeled pile penetration in Bothkennar clay, validating the numerical model against field experiments. Comparative analysis revealed the explicit time integration method as more robust and computationally efficient, particularly for complex soil–pile interactions with higher friction coefficients.

The present thesis describes the development of a computational method for the numerical simulation of compressible flows in aerodynamics. The main goal is to study high-order discretization schemes that can potentially deliver a better computational efficiency. The spatial part of the conservation equations is discretized with the finite difference method. In particular, Summation By Parts (SBP) finite difference operators and treatment of boundary conditions via Simultaneous Approximation Terms (SAT) have been investigated. An SBP finite difference operator is essentially a (high-order) centered finite difference scheme with a specific closure at the boundary. The SAT are penalty-like terms that enforce the boundary conditions weakly and are used to augment the SBP schemes. The combination of SBP operators with SAT boundary terms constitutes schemes that, for the linearized equations governing a smooth flow, are provably stable (thus convergent) schemes. The discretization in time is carried out with high-order schemes as well. Both implicit and explicit time integration schemes have been investigated. The system of non-linear equations that arises when using the implicit time integration schemes is solved via (a damped) Newton's method. On the target grid, the initial guess required for Newton's method is obtained by performing grid sequencing combined a series of explicit relaxation iterations on each grid level. The flow equations and the equation of the turbulence model (if present) are solved in a fully-coupled manner. Numerical simulations for inviscid flow, laminar flow, as well as simulations based on DNS, LES and RANS have been performed. Results show that the described computational method is particularly well-suited for smooth external flows about relatively simple geometries, solved with the DNS and LES approach. For these types of flows the gain in efficiency obtained by using high-order schemes is clear (more than a factor of 5). For RANS, however, the comparison with a state-of-the-art second order finite volume code suggests that solving the turbulence and the flow equations fully coupled with implicit schemes may not be the most efficient iteration strategy. On the other hand, the numerical simulations of non-smooth/internal flows highlighted the need of further development of the SBP-SAT framework.

Describes simulations of impact forging processes. Uses the explicit time integration finite element method, which is based on direct time integration of equation of motion, to compute the deformation of the workpiece and the dies. Uses the program developed to simulate the copper blow test performed on a 350,000J counter‐blow hammer. The calculated result reveals a good agreement in the final deformed configurations between the experiment and the explicit simulation. In order to compare this with the explicit method, the implicit time integration rigid‐plastic finite element program considering the inertia effect is also applied to the copper blow test simulation. As a result of the copper blow test simulation using the explicit program and the implicit program, finds that the calculated results have good agreements in available plastic deformation energy, forging load and equivalent plastic strain distribution. Finally, applies the developed program to simulations of multi‐blow forging processes. Presents three major findings from the multi‐blow forging simulations: (1) the continuous analysis technique used for the multi‐blow forging simulations works well; (2) the blow efficiency and the forging load generated by blow operations can be analysed efficiently and simulated results coincide with previous experimental and analytical ones; (3) the geometrical configuration of the workpiece is closely related to blow efficiency.

In this paper high order time integration schemes are investigated for the integration of uid-structure interaction (FSI) model problem with deforming domains. The integration algorithm consists of a partitioned scheme in which a combination of implicit and explicit (IMEX) high order Runge-Kutta time integration schemes is used: the uid and structure systems are decoupled at their interface and both systems are integrated using the implicit system under a given boundary condition at the interface. The inuence of this boundary condition (the coupling term) is integrated using the explicit Runge-Kutta scheme. The uid dynamics are written in the arbitrary Lagrange Eulerian formulation to cope with the deforming uid mesh. An expression is proposed for the mesh face velocities of the deforming mesh such that the discrete geometric conservation law is satised. For the model problem numerical investigations are made into the eciency of these high order time integration schemes compared to lower order methods. The IMEX scheme retains the order of the implicit and explicit schemes and obtains the same accuracy as a second order staggered scheme for less computational work.