Numerical Local Time Stepping Solutions for Transient Statistical Energy Analysis

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Oriol Guasch ◽  
Carlos García
Keyword(s):  
Finite Difference ◽  
Local Time ◽  
Energy Analysis ◽  
Blow Up ◽  
Statistical Energy Analysis ◽  
Time Step ◽  
Time Step Size ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Forward Euler

Subsystem energies evolve in transient statistical energy analysis (TSEA) according to a linear system of ordinary differential equations (ODEs), which is usually numerically solved by means of the forward Euler finite difference scheme. Stability requirements pose limits on the maximum time step size to be used. However, it has been recently pointed out that one should also consider a minimum time step limit, if time independent loss factors are to be assumed. This limit is based on the subsystem internal time scales, which rely on their characteristic mean free paths and group velocities. In some cases, these maximum and minimum limits become incompatible, leading to a blow up of the forward Euler solution. It is proposed to partially mitigate this problem by resorting to a local time-stepping finite difference strategy. Subsystems are grouped into sets characterized by different time step sizes and evolve according to them.

scholarly journals Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. T67-T77 ◽  
Author(s):  
Sara Minisini ◽  
Elena Zhebel ◽  
Alexey Kononov ◽  
Wim A. Mulder
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Heterogeneous Media ◽  
Small Scale ◽  
Time Step ◽  
Element Discretization ◽  
Time Stepping ◽  
Local Time Stepping

Modeling and imaging techniques for geophysics are extremely demanding in terms of computational resources. Seismic data attempt to resolve smaller scales and deeper targets in increasingly more complex geologic settings. Finite elements enable accurate simulation of time-dependent wave propagation in heterogeneous media. They are more costly than finite-difference methods, but this is compensated by their superior accuracy if the finite-element mesh follows the sharp impedance contrasts and by their improved efficiency if the element size scales with wavelength, hence with the local wave velocity. However, 3D complex geologic settings often contain details on a very small scale compared to the dominant wavelength, requiring the mesh to contain elements that are smaller than dictated by the wavelength. Also, limitations of the mesh generation software may produce regions where the elements are much smaller than desired. In both cases, this leads to a reduction of the time step required to solve the wave propagation and significantly increases the computational cost. Local time stepping (LTS) can improve the computational efficiency and speed up the simulation. We evaluated a local formulation of an LTS scheme with second-order accuracy for the discontinuous Galerkin finite-element discretization of the wave equation. We tested the benefits of the scheme by considering a geologic model for a North-Sea-type example.

scholarly journals Local time stepping with adaptive time step control for a two-phase fluid system

2009 ◽  
Vol 29 ◽  
pp. 73-88 ◽  
Author(s):  
Frédéric Coquel ◽  
Quang Long Nguyen ◽  
Marie Postel ◽  
Quang Huy Tran
Keyword(s):  
Local Time ◽  
Time Step ◽  
Fluid System ◽  
Two Phase ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Adaptive Time Step ◽  
Adaptive Time ◽  
Step Control ◽  
Phase Fluid

scholarly journals Construction and convergence analysis of conservative second order local time discretisation for linear wave equations

2021 ◽  
Author(s):  
Juliette Chabassier ◽  
Sébastien Imperiale
Keyword(s):  
Local Time ◽  
Wave Equations ◽  
Second Order ◽  
Linear Wave ◽  
Time Step ◽  
Time Stepping ◽  
Time Discretisation ◽  
Regularity Properties ◽  
Local Time Stepping ◽  
Linear Wave Equations

In this work we present and analyse a time discretisation strategy for linear wave equations that aims at using locally in space the most adapted time discretisation among a family of implicit or explicit centered second order schemes. The proposed family of schemes is adapted to domain decomposition methods such as the mortar element method. They correspond in that case to local implicit schemes and to local time stepping. We show that, if some regularity properties of the solution are satisfied and if the time step verifies a stability condition, then the family of proposed time discretisations provides, in a strong norm, second order space-time convergence. Finally, we provide 1D and 2D numerical illustrations that confirm the obtained theoretical results and we compare our approach on 1D test cases to other existing local time stepping strategies for wave equations.

scholarly journals High order explicit local time stepping methods for hyperbolic conservation laws

2020 ◽  
Vol 89 (324) ◽  
pp. 1807-1842
Author(s):  
Thi-Thao-Phuong Hoang ◽  
Lili Ju ◽  
Wei Leng ◽  
Zhu Wang
Keyword(s):  
Conservation Laws ◽  
Local Time ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Hyperbolic Conservation ◽  
Time Stepping ◽  
Local Time Stepping

Time-accurate local time stepping method based on flux updating

AIAA Journal ◽  
1994 ◽  
Vol 32 (9) ◽  
pp. 1926-1929 ◽  
Author(s):  
X. D. Zhang ◽  
J.-Y. Trepanier ◽  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Local Time ◽  
Time Stepping ◽  
Local Time Stepping

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

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