Pathwise approximation and simulation for the Zakai filtering equation through operator splitting

CALCOLO ◽  
1993 ◽  
Vol 30 (3) ◽  
pp. 219-239 ◽  
Author(s):  
M. Sun ◽  
R. Glowinski
Keyword(s):  
Operator Splitting ◽  
Pathwise Approximation

POSITIVITY OF k-EPSILON TURBULENCE MODELS FOR INCOMPRESSIBLE FLOW

2002 ◽  
Vol 12 (03) ◽  
pp. 393-406 ◽  
Author(s):  
ZI-NIU WU ◽  
SONG FU
Keyword(s):  
Reynolds Number ◽  
Point Source ◽  
Incompressible Flow ◽  
Iterative Procedure ◽  
High Reynolds Number ◽  
Operator Splitting ◽  
Turbulence Models ◽  
Diffusion Equations ◽  
Advection Diffusion ◽  
High Reynolds

The k-epsilon turbulence model for incompressible flow involves two advection–diffusion equations plus point-source terms. We propose a new method for positivity analysis. This method uses an iterative procedure combined with an operator splitting. With this method we recover the well-known positivity result for the standard high Reynolds number model. Most importantly, we are able to prove the positivity result for general low Reynolds number k-epsilon models.

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