Performance of a Three-Substep Time Integration Method on Structural Nonlinear Seismic Analysis

In this work, a study of a three substeps’ implicit time integration method called the Wen method for nonlinear finite element analysis is conducted. The calculation procedure of the Wen method for nonlinear analysis is proposed. The basic algorithmic property analysis shows that the Wen method has good performance on numerical dissipation, amplitude decay, and period elongation. Three nonlinear dynamic problems are analyzed by the Wen method and other competitive methods. The result comparison indicates that the Wen method is feasible and efficient in the calculation of nonlinear dynamic problems. Theoretical analysis and numerical simulation illustrate that the Wen method has desirable solution accuracy and can be a good candidate for nonlinear dynamic problems.

One-Parameter Controlled Non-Dissipative Unconditionally Stable Explicit Structure-Dependent Integration Methods with No Overshoot

Although many families of integration methods have been successfully developed with desired numerical properties, such as second order accuracy, unconditional stability and numerical dissipation, they are generally implicit methods. Thus, an iterative procedure is often involved for each time step in conducting time integration. Many computational efforts will be consumed by implicit methods when compared to explicit methods. In general, the structure-dependent integration methods (SDIMs) are very computationally efficient for solving a general structural dynamic problem. A new family of SDIM is proposed. It exhibits the desired numerical properties of second order accuracy, unconditional stability, explicit formulation and no overshoot. The numerical properties are controlled by a single free parameter. The proposed family method generally has no adverse disadvantage of unusual overshoot in high frequency transient responses that have been found in the currently available implicit integration methods, such as the WBZ-α method, HHT-α method and generalized-α method. Although this family method has unconditional stability for the linear elastic and stiffness softening systems, it becomes conditionally stable for stiffness hardening systems. This can be controlled by a stability amplification factor and its unconditional stability is successfully extended to stiffness hardening systems. The computational efficiency of the proposed method proves that engineers can do the accurate nonlinear analysis very quickly.

A Novel Improved Coupled Dynamic Solid Boundary Treatment for 2D Fluid Sloshing Simulation

In order to achieve stable and accurate sloshing simulations with complex geometries using Smoothed Particle Hydrodynamic (SPH) method, a novel improved coupled dynamic solid boundary treatment (SBT) is proposed in this study. Comparing with the previous SBT algorithms, the new SBT algorithm not only can reduce numerical dissipation, but also can greatly improve the ability to prevent fluid particles penetration and to expand the application to model unidirectional deformable boundary. Besides the new SBT algorithm, a number of modified algorithms for correcting density field and position shifting are applied to the new SPH scheme for improving numerical stability and minimizing numerical dissipation in sloshing simulations. Numerical results for three sloshing cases in tanks with different geometries are investigated in this study. In the analysis of the wave elevation and the pressure on the tank, the SPH simulation with the new SBT algorithm shows a good agreement with the experiment and the simulations using the commercial code STAR-CCM+. Especially, the sloshing case in the tank with deformable bottom demonstrates the robustness of the new boundary method.

Plume spreading test case for coastal ocean models

We present a test case of river plume spreading to evaluate numerical methods used in coastal ocean modeling. It includes an estuary–shelf system whose dynamics combine nonlinear flow regimes with sharp frontal boundaries and linear regimes with cross-shore geostrophic balance. This system is highly sensitive to physical or numerical dissipation and mixing. The main characteristics of the plume dynamics are predicted analytically but are difficult to reproduce numerically because of numerical mixing present in the models. Our test case reveals the level of numerical mixing as well as the ability of models to reproduce nonlinear processes and frontal zone dynamics. We document numerical solutions for the Thetis and FESOM-C models on an unstructured triangular mesh, as well as ones for the GETM and FESOM-C models on a quadrilateral mesh. We propose an analysis of simulated plume spreading which may be useful in more general studies of plume dynamics. The major result of our comparative study is that accuracy in reproducing the analytical solution depends less on the type of model discretization or computational grid than it does on the type of advection scheme.

Investigation on the effects of vertical baffles on liquid sloshing based on a particle method

This study adopts the numerical simulations of Moving Particle Semi-Implicit Methods (MPS), which are meshless methods based on Lagrange particles. Using Lagrange particle has an advantage that it can avoid numerical dissipation problems without directly discretizing the convection term in the governing equation. First of all, a numerical model of a liquid sloshing tank without baffles is used to confirm the effectiveness of the MPS by comparing the numerical results with the experimental data of Kang and Li. And the pressure curves obtained with MPS method were in good agreement with the experimental findings, which confirmed its effectiveness. On that basis, simulations of liquid sloshing movements with one baffle, two symmetrical baffles, and three baffles are performed, respectively. The results indicate that the addition of vertical baffles in the tanks effectively enhanced the ability to reduce liquid sloshing.

Assessment of a Discontinuous Galerkin Method for the Simulation of the Turbulent Flow around the DrivAer Car Model

The turbulent flow over the DrivAer fastback model is here investigated with an order-adaptive discontinuous Galerkin (DG) method. The growing need of high-fidelity flow simulations for the accurate determination of problems, e.g., vehicle aerodynamics, promoted research on models and methods to improve the computational efficiency and to bring the practice of Scale Resolving Simulations (SRS), like the large-eddy simulation (LES), to an industrial level. An appealing choice for SRS is the Implicit LES (ILES) via a high-order DG method, where the favourable numerical dissipation of the space discretization scheme plays directly the role of a subgrid-scale model. Implicit time integration and the p-adaptive algorithm reduce the computational cost allowing a high-fidelity description of the physical phenomenon with very coarse mesh and moderate number of degrees of freedom. Two different models have been considered: (i) a simplified DrivAer fastback model, without the rear-view mirrors and the wheels, and a smooth underbody; (ii) the DrivAer fastback model, without rear-view mirrors and a smooth underbody. The predicted results have been compared with experimental data and CFD reference results, showing a good agreement.

Optimization of a Class of n-Sub-Step Time Integration Methods for Structural Dynamics

This paper develops a family of optimized [Formula: see text]-sub-step time integration methods for structural dynamics, in which the generalized trapezoidal rule is used in the first [Formula: see text] sub-steps, and the last sub-step employs [Formula: see text]-point backward difference formula. The proposed methods can achieve second-order accuracy and unconditional stability, and their degree of numerical dissipation can range from zero to one. Also, the proposed methods can achieve the identical effective stiffness matrices for all sub-steps, reducing computational costs in the analysis of linear systems. Using the spectral analysis, optimized algorithmic parameters are presented, ensuring that the proposed methods can accurately calculate different types of dynamic problems such as wave propagation, stiff and nonlinear systems. Besides, with the increase in the number of sub-steps, the accuracy of the proposed methods can be enhanced without extra workload compared with single-step methods. Numerical experiments show that the proposed methods perform better in different dynamic systems.