Admissible Wave Fans and the Riemann Problem

2009 ◽  
pp. 271-324
Author(s):  
Constantine M. Dafermos
Keyword(s):  
Riemann Problem

Generalized Riemann problem-based upwind scheme for the vorticity transport equations

2016 ◽  
Vol 132 ◽  
pp. 10-18 ◽  
Author(s):  
Eric Parish ◽  
Karthik Duraisamy ◽  
Praveen Chandrashekar
Keyword(s):  
Riemann Problem ◽  
Transport Equations ◽  
Upwind Scheme ◽  
Generalized Riemann Problem ◽  
Vorticity Transport

Solution of the Riemann Problem in magnetogasdynamics

2014 ◽  
Vol 67 ◽  
pp. 326-330 ◽  
Author(s):  
R. Singh ◽  
L.P. Singh
Keyword(s):  
Riemann Problem

scholarly journals Surface Evolution During Semiconductor Processing

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 379-384 ◽  
Author(s):  
Ganesh Rajagopalan ◽  
Vadali Mahadev ◽  
Timothy S. Cale
Keyword(s):  
Riemann Problem ◽  
Surface Profile ◽  
Numerical Implementation ◽  
Jump Conditions ◽  
Semiconductor Processing ◽  
Explicit Integration ◽  
Surface Evolution ◽  
Left And Right ◽  
The Right ◽  
Surface Angle

We discuss our approach to using the Riemann problem to compute surface profile evolution during the simulation of deposition, etch and reflow processes. Each pair of segments which represents the surface is processed sequentially. For cases in which both segments are the same material, the Riemann problem is solved. For cases in which the two segments are different materials, two Riemann problems are solved. The material boundary is treated as the right segment for the left material and as the left segment for the right material. The critical equations for the analyses are the characteristics of the Riemann problem and the ‘jump conditions’ which represent continuity of the surface. Examples are presented to demonstrate selected situations. One limitation of the approach is that the velocity of the surface is not known as a function of the surface angle. Rather, it is known for the angles of the left and right segments. The rate as a function of angle must be assumed for the explicit integration procedure used. Numerical implementation is briefly discussed.

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