A RELAXATION METHOD VIA THE BORN-INFELD SYSTEM

被引:2
作者
Tran, Quang Huy [1 ]
Baudin, Michael [1 ]
Coquel, Frederic [2 ]
机构
[1] IFP, Dept Math Appl, F-92852 Rueil Malmaison, France
[2] Univ Paris 06, CNRS, Lab Jacques Louis Lions, F-75252 Paris 05, France
关键词
Conservation laws; relaxation methods; Born-Infeld system; two-phase flow; HYPERBOLIC CONSERVATION-LAWS; 2-PHASE FLOW; MODEL; FLUX; EQUATIONS; SCHEMES; ENERGY;
D O I
10.1142/S0218202509003760
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The semilinear relaxation was introduced by Jin and Xin [Comm. Pure Appl. Math. 48, 235, (1995)] in order to approximate the conservation law partial derivative(t)u + partial derivative(x)f(u) = 0 for any flux function f is an element of l(1) (R; R). In this paper, we propose an alternative relaxation technique for scalar conservation laws of the form partial derivative(t)u + partial derivative(x)u(1 - u)g(u) = 0, where g is an element of l(1) ([0, 1]; R) and 0 is not an element of g(]0, 1[). We extend this new philosophy to an arbitrary flux function f whenever possible. Unlike the semilinear approach, the new relaxation strategy does not involve any tuning parameter, but makes use of the Born-Infeld system. Another advantage of this method is that it enables us to achieve a maximum principle on the velocities omega = (1 - u)g and z = -ug, which turns out to be a physically interesting and helpful feature in the context of some two-phase flow problems.
引用
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页码:1203 / 1240
页数:38
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