The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions asso-5 ciated with Lagrange polynomials based on Gauss–Lobatto–Legen...

We present the large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method (SEM) using three subgrid-scale models. Two spectral filtering techniques suitable for these simulations have been implemented. Numerical results for Reynolds number Re = 12.000 are showing very good agreement with the Direct Numerical Simulation (DNS) results and relatively good agreement wi...

As detailed in recent reports [2 §1; 3; & op. cit. therein], a need has long been well established and many investigations undertaken at NCAR and elsewhere, to create high-resolution numerical simulation methods for atmospheric dynamics, that are accurate similarly to spectral methods and computationally efficient similarly to finite-element type methods. Two research codes that demonstrate the...

We introduce a novel spectral element method based on the ultraspherical and hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations polygonal domains with unstructured quadrilateral or triangular meshes. Properties of lead to almost banded systems, allowing be competitive in high-polynomial regime ($p > 5$). The enables precomputed solution opera...

Abstract. Among many structural health monitoring (SHM) methods, guided wave (GW) based method has been found as an effective and efficient way to detect incipient damages. In comparison with other widely used SHM methods, it can propagate in a relatively long range and be sensitive to small damages. Proper use of this technique requires good knowledge of the effects of damage on the wave chara...

The celebrated Spectral Element Method (SEM) has appeared to be of great interest to extend the capabilities of spectral methods to complex geometries. However, using quadrangular (hexahedral in 3D) elements may be a severe restriction for the most complex geometries, because requiring a structured mesh. Thus, Finite element meshes are usually based on triangles (tetrahedra in 3D). Efforts have...

We present a simple filtering procedure for stabilizing the spectral element method (SEM) for the unsteady advection-diffusion and Navier-Stokes equations. A number of example applications are presented, along with basic analysis for the advection-diffusion case. Stabilisation par filtrage pour la méthode des éléments spectraux Résumé. Nous présentons une procédure simple de filtrage pour la st...

The goal of this paper is to investigate the spectral element method (SEM), a grid-based computational approach, and the grid-free particle strength exchange method (PSEM) for solving the advection-diffusion-reaction equation in a microfluidic channel. We identify the dimensionless parameter regimes at which each algorithm provides a satisfactory solution in terms of accuracy and computational ...

We address the Korteweg-de Vries equation as an interesting model of high order partial differential equation, and show that using the classical spectral element method, i.e. a high order continuous Galerkin approximation, it is possible to develop satisfactory schemes, in terms of accuracy, computational efficiency, simplicity of implementation and, if required, conservation of the lower invar...