On the numerical convergence and performance of different spatial discretization techniques for transient elastodynamic wave propagation problems

We present a systematic investigation of several discretization approaches for transient elastodynamic wave propagation problems. This comparison includes a Finite Difference, a Finite Volume, a Finite Element, a Spectral Element and the Scaled Boundary Finite Element Method. Numerical examples are given for simple geometries with normalized parameters, for heterogeneous materials as well as for structures with arbitrarily shaped material interfaces. General conclusions regarding the accuracy of the methods are presented. Based on the essential numerical examples an expansion of the results to a wide range of problems and thus to numerous fields of application is possible.     

An efficient matrix solver for finite-element analysis of non-Newtonian fluid flow problems

When the Galerkin finite-element method with a nine-node isoparametric Lagrangian element is applied to solve non-Newtonian fluid flow problems, a considerable amount of computing time is required to solve the discretized non-linear system of equations by Newton's method. A method proposed by Broyden has been modified to compute the Jacobian matrix associated with Newton's method. This modified Broyden's method can be combined with the frontal method to efficiently solve the linearized finite-element equations during the iteration. Numerical results of a sample problem concerning the determination of the pressure-drop/flow-rate relationship for power-law fluids in rectangular ducts show that the application of this new method can reduce computing time substantially.     

Nonlinear vertical accelerations of a floating torus in regular waves

The longitudinal motions and vertical accelerations of a floating torus as well as wave motion inside the torus are studied by model tests in regular deep-water waves. Comparisons are made with linear and partly with second-order potential-flow theory for the smallest examined experimental wave height-to-wave length ratio 1/120. Reasonable agreement is obtained, in particular for the linear problem. The importance of 3D flow, hydroelasticity and strong hydrodynamic frequency dependency is documented. Experimental precision errors and bias errors, for instance, due to tank-wall interference are discussed. Numerical errors due to viscous effects are found to be secondary. Experiments show that the third and fourth harmonic accelerations of the torus matter and cannot be explained by a perturbation method with the wave steepness as a small parameter.     

Computation of wave fields in the ocean around an Isaland

A linear wave equation correct to first order in bed slope is used to calculate the wave field in the sea around an idealized island. This is of circular cylindrical shape and is situated on a paraboloidal shoal in an ocean of constant depth (Figure 1). The sides of the island are assumed fully reflecting. The incident waves are plane and periodic. Wave periods up to 30 min are investigated, and the Coriolis force is neglected. The solution of the wave equation is represented by a finite Fourier series, and a large number of very accurate numerical computations are carried through. The results appear partly in figures showing amplitude and phase angle curves (in some cases extending to the water area of constant depth outside the shoal), partly in figures showing amplitude vs wave period in fixed points. Comparison with solutions to the linearized long-wave equation is made, and the validity range of the corresponding shallow water theory is given. The influence of the shoal is studied by investigating the wave field around an island in an ocean of constant depth. New criteria are given for the applicability of a geometrical optics approach (i. e. refraction). Complete numerical refraction solutions for points at the shoreline (corresponding to many wave orthogonals ending at the point) for shallows water waves, as for the general case, demonstrate the inadequacy of this approach for long-period waves (seismic seawaves: tsunamis). All non-linear effects, including dissipation, are excluded.     

两斜交圆柱壳应力分析的边界元法

本文研究了两斜交圆柱壳的边界元法。提出了用板的基本解叠加级数形式的修正项构成圆柱壳的基本解,提高了计算精度,缩短了计算时间。对区域积分进行特殊处理,从而避免了内部网格的划分,大大减少了数据准备工作量和占机内存。并编制了FORTRAN计算程序,进行了数值计算。