Reducing spurious oscillations in discontinuous wave propagation simulation using high-order finite elements

Abstract

a b s t r a c tIn this paper, a modified explicit time integration scheme is proposed for simulating the propagation of discontinuous waves. The spatial domain is discretized by the finite element method. To obtain accurate results, the standard finite element method requires a very fine mesh, which is why the computational effort can be very time consuming. The use of high-order finite element methods -such as the spectral element method based on Lagrange polynomials through Gauss-Lobatto-Legendre points or the iso-geometric analysis using non-uniform rational B-splines -can reduce the enormous computational costs significantly, compared to the standard finite element method. However, explicit time integration schemes such as the central difference method cannot eliminate the spurious oscillation near the front wave. The procedure proposed here is basically similar to the explicit method of Noh and Bathe, but the semi-discrete equation of motion is modified by introducing a damping parameter to suit the high-order FEM analysis of the discontinuous wave propagation. The performance due to this modification is tested for one-dimensional wave propagation problems using both lumped and consistent mass matrices. Then, the idea of a combination of the consistent and row sum lumped mass matrices is evaluated. The proposed method is studied also in two-dimensions by considering the Lamb problem of wave propagation. The results are promising enough to provide a better simulation of the discontinuous wave propagation problem.

Ultrasonic Guided Wave Propagation through Welded Lap Joints

“…The ANSYS finite element software was used to obtain wave propagation through the 2D geometry which includes an implicit algorithm with Newmark time integration method for solving the transient wave propagation. The model of elastic wave propagation is based on the assumption of linear elasticity and solution of the Navier equation of the elastic wave motion in matrix form [38][39][40][41][42][43][44]:…”

High‐order isogeometric modified method of characteristics for two‐dimensional coupled Burgers' equations

“…On the other hand, the solution obtained using the quartic polynomial is in good agreement with the exact solution for this case with . Note that at high Reynolds numbers, the convection terms in the Burgers system (1) become highly dominant for which nonphysical oscillations are expected when using high polynomial orders in the discretization, see for example References 1,40. This is not the case in the proposed isogeometric modified method of characteristics mainly because (i) the modified method of characteristics is proven to be unconditionally stable, see for instance References 41‐43, and (ii) the potential of the k ‐refinement strategy in offering high inter‐element continuity by providing smoother functions than the conventional finite element methods, see References 24,25,44 among others.…”

The simulation of transport processes in cementitious materials with embedded healing systems

“…In the present work, a different approach is employed, in which the storage matrix is computed as an interpolation between the mass-distributed and mass-lumped matrices. This is similar to the approach of Mirbagheri et al 87 who applied a higher order mass matrix to a discontinuous wave propagation problem to dampen spurious oscillations (see also Wu and Qiu, 88 and Wang et al 89 ). This leads to:…”