Poisson bracket formulation of incompressible flow equations in continuum mechanics

1990 ◽  
Vol 34 (1) ◽  
pp. 55-78 ◽  
Author(s):  
A. N. Beris ◽  
B. J. Edwards
Keyword(s):  
Poisson Bracket ◽  
Continuum Mechanics ◽  
Incompressible Flow ◽  
Flow Equations

Dilation-free solutions for the incompressible flow equations on nonstaggered grids

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 585-586
Author(s):  
P. A. Russell ◽  
S. Abdallah
Keyword(s):  
Incompressible Flow ◽  
Flow Equations

A Jacobian-Free Newton Krylov Implicit-Explicit Time Integration Method for Incompressible Flow Problems

2013 ◽  
Vol 13 (5) ◽  
pp. 1408-1431 ◽  
Author(s):  
Samet Y. Kadioglu ◽  
Dana A. Knoll
Keyword(s):  
Incompressible Flow ◽  
Time Integration ◽  
Order Reduction ◽  
Second Order ◽  
Navier Stokes ◽  
Function Evaluation ◽  
Flow Equations ◽  
Flow Problems ◽  
Specific Operator ◽  
Time Accuracy

AbstractWe have introduced a fully second order IMplicit/EXplicit (IMEX) time in-tegration technique for solving the compressible Euler equations plus nonlinear heat conduction problems (also known as the radiation hydrodynamics problems) in Kadioglu et al., J. Comp. Physics [22,24]. In this paper, we study the implications when this method is applied to the incompressible Navier-Stokes (N-S) equations. The IMEX method is applied to the incompressible flow equations in the following manner. The hyperbolic terms of the flow equations are solved explicitly exploiting the well understood explicit schemes. On the other hand, an implicit strategy is employed for the non-hyperbolic terms. The explicit part is embedded in the implicit step in such a way that it is solved as part of the non-linear function evaluation within the framework of the Jacobian-Free Newton Krylov (JFNK) method [8,29,31]. This is done to obtain a self-consistent implementation of the IMEX method that eliminates the potential order reduction in time accuracy due to the specific operator separation. We employ a simple yet quite effective fractional step projection methodology (similar to those in [11,19,21,30]) as our preconditioner inside the JFNK solver. We present results from several test calculations. For each test, we show second order time convergence. Finally, we present a study for the algorithm performance of the JFNK solver with the new projection method based preconditioner.

scholarly journals SYMPLECTIC GEOMETRY AND HAMILTONIAN FLOW OF THE RENORMALIZATION GROUP EQUATION

1995 ◽  
Vol 10 (18) ◽  
pp. 2703-2732 ◽  
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Renormalization Group ◽  
Phase Space ◽  
Poisson Bracket ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Identity Operator ◽  
Group Equation ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Group Flow

It is argued that renormalization group flow can be interpreted as a Hamiltonian vector flow on a phase space which consists of the couplings of the theory and their conjugate “momenta,” which are the vacuum expectation values of the corresponding composite operators. The Hamiltonian is linear in the conjugate variables and can be identified with the vacuum expectation value of the trace of the energy-momentum operator. For theories with massive couplings the identity operator plays a central role and its associated coupling gives rise to a potential in the flow equations. The evolution of any quantity, such as N-point Green functions, under renormalization group flow can be obtained from its Poisson bracket with the Hamiltonian. Ward identities can be represented as constants of the motion which act as symmetry generators on the phase space via the Poisson bracket structure.

Evaluation of an unfactored method for the solution of the incompressible flow equations using artificial compressibility

1998 ◽  
Vol 20 (3) ◽  
pp. 179-187 ◽  
Author(s):  
R.M. Gatiganti ◽  
K.J. Badcock ◽  
F. Cantariti ◽  
L. Dubuc ◽  
M. Woodgate ◽  
...  
Keyword(s):  
Incompressible Flow ◽  
Artificial Compressibility ◽  
Flow Equations
Sign in / Sign up

Export Citation Format

Share Document