An adaptive numerical method for solving EDQNM equations for the analysis of long-time decay of isotropic turbulence

2014 ◽  
Vol 262 ◽  
pp. 72-85 ◽  
Author(s):  
M. Meldi ◽  
P. Sagaut
Keyword(s):  
Numerical Method ◽  
Isotropic Turbulence ◽  
Time Decay ◽  
Long Time ◽  
Adaptive Numerical Method

scholarly journals Global small data solutions for semilinear waves with two dissipative terms

2021 ◽  
Author(s):  
Wenhui Chen ◽  
Marcello D’Abbicco ◽  
Giovanni Girardi
Keyword(s):  
Wave Equations ◽  
Space Dimension ◽  
Full Range ◽  
Small Data ◽  
Decay Estimates ◽  
Time Decay ◽  
Nonexistence Result ◽  
Derivative Type ◽  
Long Time ◽  
Dissipative Terms

AbstractIn this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity $$|u|^p$$ | u | p or nonlinearity of derivative type $$|u_t|^p$$ | u t | p , in any space dimension $$n\geqslant 1$$ n ⩾ 1 , for supercritical powers $$p>{\bar{p}}$$ p > p ¯ . The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive $$L^r-L^q$$ L r - L q long time decay estimates for the solution in the full range $$1\leqslant r\leqslant q\leqslant \infty $$ 1 ⩽ r ⩽ q ⩽ ∞ . The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers $$p<{\bar{p}}$$ p < p ¯ .

scholarly journals Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jamel Benameur ◽  
Mongi Blel
Keyword(s):  
Global Solution ◽  
Time Decay ◽  
Long Time

We study the behavior at infinity in time of any global solutionθ∈C(R+,Ḣ2-2α(R2))of the surface quasigeostrophic equation with subcritical exponent2/3≤α≤1. We prove thatlim⁡t→∞∥θ(t)∥Ḣ2-2α=0. Moreover, we prove also the nonhomogeneous version of the previous result, and we prove that ifθ∈C(R+,Ḣ2-2α(R2))is a global solution, thenlim⁡t→∞∥θ(t)∥H2-2α=0.

scholarly journals A conservative fully-discrete numerical method for the regularised shallow water wave equations

2021 ◽  
Author(s):  
Dimitrios Mitsotakis ◽  
Hendrik Ranocha ◽  
David I Ketcheson ◽  
Endre Süli
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Numerical Method ◽  
Solitary Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Mixed Finite Element ◽  
Boussinesq System ◽  
Fully Discrete ◽  
Long Time

The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and reflective boundary conditions. The particular system is one of a class of equations derived recently and can be used in practical simulations to describe the propagation of weakly nonlinear and weakly dispersive long water waves, such as tsunamis. Studies of small-amplitude long waves usually require long-time simulations in order to investigate scenarios such as the overtaking collision of two solitary waves or the propagation of transoceanic tsunamis. For long-time simulations of non-dissipative waves such as solitary waves, the preservation of the total energy by the numerical method can be crucial in the quality of the approximation. The new conservative fully-discrete method consists of a Galerkin finite element method for spatial semidiscretisation and an explicit relaxation Runge--Kutta scheme for integration in time. The Galerkin method is expressed and implemented in the framework of mixed finite element methods. The paper provides an extended experimental study of the accuracy and convergence properties of the new numerical method. The experiments reveal a new convergence pattern compared to standard Galerkin methods.

scholarly journals Evidence of current stabilization after long-time decay in high-TC superconductors

Cryogenics ◽  
2005 ◽  
Vol 45 (2) ◽  
pp. 135-140 ◽  
Author(s):  
H. González-Jorge ◽  
J. Peleteiro ◽  
J. Troncoso ◽  
E. Carballo ◽  
G. Domarco
Keyword(s):  
Time Decay ◽  
High Tc Superconductors ◽  
High Tc ◽  
Long Time

scholarly journals LONG TIME SIMULATION OF A BEAM IN A PERIODIC FOCUSING CHANNEL VIA A TWO-SCALE PIC-METHOD

2009 ◽  
Vol 19 (02) ◽  
pp. 175-197 ◽  
Author(s):  
EMMANUEL FRÉNOD ◽  
FRANCESCO SALVARANI ◽  
ERIC SONNENDRÜCKER
Keyword(s):  
Electric Field ◽  
Numerical Method ◽  
External Electric Field ◽  
Time Scales ◽  
Asymptotic State ◽  
Limit Model ◽  
Time Simulation ◽  
Charged Beam ◽  
Long Time ◽  
Pic Method

We study the two-scale asymptotics for a charged beam under the action of a rapidly oscillating external electric field. After proving the convergence to the correct asymptotic state, we develop a numerical method for solving the limit model involving two time scales and validate its efficiency for the simulation of long time beam evolution.

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