An Efficient High-Order Time Integration Method for Spectral-Element Discontinuous Galerkin Simulations in Electromagnetics

2013 ◽  
Vol 57 (3) ◽  
pp. 582-603 ◽  
Author(s):  
Misun Min ◽  
Paul Fischer
Keyword(s):  
Discontinuous Galerkin ◽  
Integration Method ◽  
Time Integration ◽  
Spectral Element ◽  
High Order ◽  
Time Integration Method ◽  
High Order Time

scholarly journals Three-step Predictor-Corrector Finite Element Schemes for Consolidation Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Mina Torabi ◽  
Manuel Pastor ◽  
Miguel Martín Stickle
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Spectral Element ◽  
Euler Method ◽  
One Dimensional ◽  
Time Integration Method ◽  
The One ◽  
Predictor Corrector ◽  
Finite Element Schemes ◽  
First Time

An accurate, stable, and efficient three-step predictor-corrector time integration method is considered, for the first time, to obtain numerical solution for the one-dimensional consolidation equation within a finite and spectral element framework. Theoretical order of accuracy and stability conditions are provided. The three-step predictor-corrector time integration method is third-order accurate and shows a larger stability region than the forward Euler method when applied to the one-dimensional consolidation equation. Furthermore, numerical results are in agreement with analytical solutions previously derived by the authors.

scholarly journals An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation

2021 ◽  
Vol 11 (4) ◽  
pp. 1932
Author(s):  
Weixuan Wang ◽  
Qinyan Xing ◽  
Qinghao Yang
Keyword(s):  
High Frequency ◽  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Weak Form ◽  
High Accuracy ◽  
Numerical Dissipation ◽  
Frequency Range ◽  
Time Integration Method ◽  
Numerical Damping

Based on the newly proposed generalized Galerkin weak form (GGW) method, a two-step time integration method with controllable numerical dissipation is presented. In the first sub-step, the GGW method is used, and in the second sub-step, a new parameter is introduced by using the idea of a trapezoidal integral. According to the numerical analysis, it can be concluded that this method is unconditionally stable and its numerical damping is controllable with the change in introduced parameters. Compared with the GGW method, this two-step scheme avoids the fast numerical dissipation in a low-frequency range. To highlight the performance of the proposed method, some numerical problems are presented and illustrated which show that this method possesses superior accuracy, stability and efficiency compared with conventional trapezoidal rule, the Wilson method, and the Bathe method. High accuracy in a low-frequency range and controllable numerical dissipation in a high-frequency range are both the merits of the method.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

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