Central Schemes for Systems of Balance Laws

Liotta, S.F.; Romano, Vittorio; Russo, Giovanni

doi:10.1007/978-3-0348-8724-3_16

Cited by 11 publications

(18 citation statements)

References 10 publications

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“…High-order, unstructured grids and multidimensional versions can be found in [4,7,25,26,30]. Staggered central schemes for the 1D Saint-Venant system were proposed in [27]. Note that these methods do not preserve stationary steady-states.…”

Section: Introductionmentioning

confidence: 99%

Central-Upwind Schemes for the Saint-Venant System

2002

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Abstract. We present one-and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes for systems of hyperbolic conservation laws to balance laws. Special attention is paid to the discretization of the source term such as to preserve stationary steady-state solutions. We also prove that the second-order version of our schemes preserves the nonnegativity of the height of the water. This important feature allows one to compute solutions for problems that include dry areas.Mathematics Subject Classification. 65M06, 35L65.

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Section: Introductionmentioning

confidence: 99%

Central-Upwind Schemes for the Saint-Venant System

2002

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“…The central schemes known in the literature deal almost exclusively with homogeneous systems. In [5,6] a suitable extension for one-dimensional balance laws with (possibly stiff ) source terms has been developed on the basis of the Nessyahu and Tadmor scheme [3] for homogeneous hyperbolic system. It has been applied in [22,23] to parabolic band hydrodynamical models of semiconductors.…”

Section: Methodsmentioning

confidence: 99%

“…In order to get a full second-order scheme we combine the relaxation and convective steps in the same way as proposed in [5,6] for the one-dimensional case. Note that the analysis of the splitting accuracy does not really depend on the dimension of the space.…”

Section: Methodsmentioning

confidence: 99%

“…21]), the energy flux S is not a field variable and it is not necessary to prescribe boundary conditions for it. The relations (36) 4 and (37) 5 are not based on the microscopic boundary conditions for the distribution function, but they may be justified in a heuristic way with the same approach that was followed in [35].…”

Section: Simulation Of a Silicon Mesfetmentioning

confidence: 99%

“…A numerical scheme for problems of this kind based on central differencing has been developed in [5,6,22] for the one-dimensional case and applied in [7,9] to bulk silicon and to an n + -n-n + silicon diode (for the parabolic band case see [23]). The obtained results are rather encouraging regarding the accuracy of the model and the performance of the numerical scheme.…”

Section: Introductionmentioning

confidence: 99%

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2D Simulation of a Silicon MESFET with a Nonparabolic Hydrodynamical Model Based on the Maximum Entropy Principle

Romano¹

2002

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Asymptotic Waves in the Hydrodynamical Model of Semiconductors Based on Extended Thermodynamics

Romano

Torrisi

2001

Z. angew. Math. Mech.

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An analysis of asymptotic wave solutions for the hydrodynamical model of semiconductors based on Extended Thermodynamics [1, 2, 3, 4] is presented. The evolution equations form a quasilinear hyperbolic system, coupled to the Poisson equation for the electric potential. The aim of this article is to describe the far field for such a model by a suitable adaptation of the asymptotic expansion proposed in [5, 6, 7]. The stationary solution for uniformly doped semiconductor has been taken as unperturbed state. We distinguish two cases: perturbations with wavelength smaller than the scaled Debye length and perturbations of the same order of the Debye length. In the first case the perturbation of the electric field is negligible and the resulting model equation exhibits nonlinear and relaxation effects. In the second case a drift term due to the presence of a non negligible perturbation of the electric field arises as well.

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Central Schemes for Systems of Balance Laws

Cited by 11 publications

References 10 publications

Central-Upwind Schemes for the Saint-Venant System

Central-Upwind Schemes for the Saint-Venant System

2D Simulation of a Silicon MESFET with a Nonparabolic Hydrodynamical Model Based on the Maximum Entropy Principle

Asymptotic Waves in the Hydrodynamical Model of Semiconductors Based on Extended Thermodynamics

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