The stability chart of parallel shear flows with double diffusive processes—approximate derivation by a first-order Galerkin method

1988 ◽  
Vol 31 (3) ◽  
pp. 525-539 ◽  
Author(s):  
M. Magen ◽  
D. Pnueli ◽  
Y. Zvirin
Keyword(s):  
Galerkin Method ◽  
Shear Flows ◽  
First Order ◽  
Stability Chart ◽  
Parallel Shear Flows ◽  
The Stability ◽  
Diffusive Processes ◽  
Double Diffusive

scholarly journals A General Numerical Method for Analyzing the Linear Stability of Stratified Parallel Shear Flows

2014 ◽  
Vol 31 (12) ◽  
pp. 2795-2808 ◽  
Author(s):  
Tim Rees ◽  
Adam Monahan
Keyword(s):  
Stability Analysis ◽  
Numerical Method ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Analytical Approximations ◽  
Onset Of Turbulence ◽  
Parallel Shear Flows ◽  
Critical Layers ◽  
The Stability ◽  
Stability Results

Abstract The stability analysis of stratified parallel shear flows is fundamental to investigations of the onset of turbulence in atmospheric and oceanic datasets. The stability analysis is performed by considering the behavior of small-amplitude waves, which is governed by the Taylor–Goldstein (TG) equation. The TG equation is a singular second-order eigenvalue problem, whose solutions, for all but the simplest background stratification and shear profiles, must be computed numerically. Accurate numerical solutions require that particular care be taken in the vicinity of critical layers resulting from the singular nature of the equation. Here a numerical method is presented for finding unstable modes of the TG equation, which calculates eigenvalues by combining numerical solutions with analytical approximations across critical layers. The accuracy of this method is assessed by comparison to the small number of stratification and shear profiles for which analytical solutions exist. New stability results from perturbations to some of these profiles are also obtained.

On the stability of parallel shear flows with embedded swirl

2021 ◽  
Vol 150 (4) ◽  
pp. A177-A177
Author(s):  
Lu Zhao ◽  
Saeed Farokhi ◽  
Ray Taghavi
Keyword(s):  
Shear Flows ◽  
Parallel Shear Flows ◽  
The Stability

scholarly journals Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell's Equations in Anisotropic Materials

2017 ◽  
Vol 21 (5) ◽  
pp. 1350-1375 ◽  
Author(s):  
Adérito Araújo ◽  
Sílvia Barbeiro ◽  
Maryam Khaksar Ghalati
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mesh Size ◽  
Element Space ◽  
First Order ◽  
Balance Accuracy ◽  
The Stability

AbstractIn this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability and error estimates, for cases of typical boundary conditions, either perfect electric, perfect magnetic or first order Silver-Müller. The bounds of the stability region point out the influence of not only the mesh size but also the dependence on the choice of the numerical flux and the degree of the polynomials used in the construction of the finite element space, making possible to balance accuracy and computational efficiency. In the model we consider heterogeneous anisotropic permittivity tensors which arise naturally in many applications of interest. Numerical results supporting the analysis are provided.

On the Stability of Parallel Shear Flows with Embedded Swirl

2022 ◽  
Author(s):  
Lu Zhao ◽  
Saeed Farokhi ◽  
Ray Taghavi
Keyword(s):  
Shear Flows ◽  
Parallel Shear Flows ◽  
The Stability

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

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