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A note on (2K+1)-point conservative monotone schemes

Huazhong Tang, Gerald Warnecke (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

First–order accurate monotone conservative schemes have good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a (2K+1)-point monotone scheme may give an oscillatory solution even...

A note on critical times of 2 × 2 quasilinear hyperbolic systems

Ivan Straškraba (1984)

Aplikace matematiky

In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a 2 × 2 quasilinear hyperbolic system is derived. The applicability of the formula in the engineering praxis is shown on one-dimensional equations of isentropic non-viscous compressible fluid flow.

A note on poroacoustic traveling waves under Darcy's law: Exact solutions

P. M. Jordan, J. K. Fulford (2011)

Applications of Mathematics

A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...

A parameter-free smoothness indicator for high-resolution finite element schemes

Dmitri Kuzmin, Friedhelm Schieweck (2013)

Open Mathematics

This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite...

A parametrix construction for wave equations with C 1 , 1 coefficients

Hart F. Smith (1998)

Annales de l'institut Fourier

In this article we give a construction of the wave group for variable coefficient, time dependent wave equations, under the hypothesis that the coefficients of the principal term possess two bounded derivatives in the spatial variables, and one bounded derivative in the time variable. We use this construction to establish the Strichartz and Pecher estimates for solutions to the Cauchy problem for such equations, in space dimensions n = 2 and n = 3 .

A positivity preserving central scheme for shallow water flows in channels with wet-dry states

Jorge Balbás, Gerardo Hernandez-Duenas (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present a high-resolution, non-oscillatory semi-discrete central scheme for one-dimensional shallow-water flows along channels with non uniform cross sections of arbitrary shape and bottom topography. The proposed scheme extends existing central semi-discrete schemes for hyperbolic conservation laws and enjoys two properties crucial for the accurate simulation of shallow-water flows: it preserves the positivity of the water height, and it is well balanced, i.e., the source terms arising from...

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