Semi-implicit donor cell differencing and the hyperbolic conservation laws having source terms

1996 ◽  
Vol 131 (1-2) ◽  
pp. 91-107 ◽  
Author(s):  
Farhad Ali ◽  
M.A. Kassar
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Donor Cell ◽  
Source Terms ◽  
Hyperbolic Conservation

HYPERBOLIC CONSERVATION LAWS HAVING SOURCE TERMS AND DONOR CELL DIFFERENCING

1994 ◽  
Vol 05 (03) ◽  
pp. 519-536 ◽  
Author(s):  
FARHAD ALI ◽  
M.A. KASSAR
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Phase Error ◽  
Stability Limit ◽  
Donor Cell ◽  
Test Problems ◽  
Source Terms ◽  
Hyperbolic Conservation ◽  
First Order ◽  
Linear Scalar

Modifications in the integration of the source terms in hyperbolic conservation laws such as those governing combustion, detonation and radiative transport, with a first order upwind differencing technique are proposed and analysed. The von Neuman stability and phase error analysis for a linear scalar equation, together with a few test problems is presented in order to compare the performance of the resulting variants of the donor cell scheme. It is established that when the source term is integrated using higher order formulae, the resulting scheme gives better resolution and has better stability limit and phase accuracy, compared to the standard single nodal value replacement. It is shown that integration by the trapezoidal rule gives sufficient accuracy and further improvement may not necessarily be achieved using better methods, such as the Simpson’s rule.

scholarly journals On Approximation of Entropy Solutions for One System of Nonlinear Hyperbolic Conservation Laws with Impulse Source Terms

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ciro D'Apice ◽  
Peter I. Kogut ◽  
Rosanna Manzo
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Dynamic Models ◽  
Optimization Problems ◽  
Fluid Dynamic ◽  
Entropy Solutions ◽  
Source Terms ◽  
Hyperbolic Conservation ◽  
Linear Evolution ◽  
Linear Evolution Equation

We study one class of nonlinear fluid dynamic models with impulse source terms. The model consists of a system of two hyperbolic conservation laws: a nonlinear conservation law for the goods density and a linear evolution equation for the processing rate. We consider the case when influx-rates in the second equation take the form of impulse functions. Using the vanishing viscosity method and the so-called principle of fictitious controls, we show that entropy solutions to the original Cauchy problem can be approximated by optimal solutions of special optimization problems.

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