Journal ArticleDOI
Central Schemes for Balance Laws of Relaxation Type
TLDR
A generalization of the Nessyahu--Tadmor scheme to the nonhomogeneous case by including the cell averages of the production terms in the discrete balance equations and a second order scheme uniformly accurate in the relaxation parameter is derived and its properties analyzed.Abstract:
Several models in mathematical physics are described by quasi-linear hyperbolic systems with source term and in several cases the production term can become stiff. Here suitable central numerical schemes for such problems are developed and applications to the Broadwell model and extended thermodynamics are presented.
The numerical methods are a generalization of the Nessyahu--Tadmor scheme to the nonhomogeneous case by including the cell averages of the production terms in the discrete balance equations. A second order scheme uniformly accurate in the relaxation parameter is derived and its properties analyzed. Numerical tests confirm the accuracy and robustness of the scheme.read more
Citations
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Journal ArticleDOI
Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).
TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Journal ArticleDOI
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Lorenzo Pareschi,Giovanni Russo +1 more
TL;DR: New implicit–explicit (IMEX) Runge–Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms are considered, with high accuracy in space and several applications are presented.
Posted Content
Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
Lorenzo Pareschi,Giovanni Russo +1 more
TL;DR: In this article, new implicit-explicit (IMEX) Runge-Kutta methods were proposed for hyperbolic systems of conservation laws with stiff relaxation terms. But the implicit part is treated by a strong-stability-preserving (SSP) scheme, and the explicit part is represented by an L-stable diagonally implicit Runge Kutta method (DIRK).
Book
Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations
Lorenzo Pareschi,Giovanni Russo +1 more
TL;DR: New implicit-explicit (IMEX) Runge Kutta methods suitable for time dependent partial differential systems which contain stiff and non stiff terms are presented and accuracy and stability properties of these schemes are studied.
Journal ArticleDOI
A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Laws
TL;DR: The heart of the method is the reconstruction step, in which a genuinely two-dimensional interpolant is reconstructed from cell averages by taking a convex combination of building blocks in the form of biquadratic polynomials.
References
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Book
Linear and Nonlinear Waves
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Book
Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems
Ernst Hairer,Gerhard Wanner +1 more
TL;DR: In this paper, the authors present the solution of stiff differential equations and differential-algebraic systems (differential equations with constraints) and discuss their application in physics, chemistry, biology, control engineering, electrical network analysis, and computer programs.
Book
Numerical methods for conservation laws
TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.
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