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Shock Profiles (shock + profile)

Distribution by Scientific Domains
Mathematics and Statistics66%
Engineering33%

Selected Abstracts

A hybrid FVM,LBM method for single and multi-fluid compressible flow problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010
Himanshu Joshi
Abstract The lattice Boltzmann method (LBM) has established itself as an alternative approach to solve the fluid flow equations. In this work we combine LBM with the conventional finite volume method (FVM), and propose a non-iterative hybrid method for the simulation of compressible flows. LBM is used to calculate the inter-cell face fluxes and FVM is used to calculate the node parameters. The hybrid method is benchmarked for several one-dimensional and two-dimensional test cases. The results obtained by the hybrid method show a steeper and more accurate shock profile as compared with the results obtained by the widely used Godunov scheme or by a representative flux vector splitting scheme. Additional features of the proposed scheme are that it can be implemented on a non-uniform grid, study of multi-fluid problems is possible, and it is easily extendable to multi-dimensions. These features have been demonstrated in this work. The proposed method is therefore robust and can possibly be applied to a variety of compressible flow situations. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Stability of travelling wave solutions to a semilinear hyperbolic system with relaxation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2009
Yoshihiro Ueda
Abstract We study a semilinear hyperbolic system with relaxation and investigate the asymptotic stability of travelling wave solutions with shock profile. It is shown that the travelling wave solution is asymptotically stable, provided the initial disturbance is suitably small. Moreover, we show that the time convergence rate is polynomially (resp. exponentially) fast as t,, if the initial disturbance decays polynomially (resp. exponentially) for x,,. Our proofs are based on the space,time weighted energy method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A numerical study of wave structures developed on the free surface of a film flowing on inclined planes and subjected to surface shear

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2006
N. H. Shuaib
Abstract In this work, we determine the different patterns of possible wave structures that can be observed on a thin film flowing on an inclined plane when at the free surface a shear force (surface traction) is applied. Different wave structures are obtained dependening on the selected combination of downstream and upstream boundary conditions and initial conditions. The resulting initial boundary value problems are solved numerically using the direct BEM numerical solution of the complete two-dimensional Stokes system of equations. In our numerical results, the initial discontinuous shock profiles joining uniform fluid depths are smoothed due to the two-dimensional character of the Stokes formulation, including the effect of the gravitational force as well as the interfacial surface tension force. In this way, physically feasible continuous surface profiles are determined, in which the initial uniform depths are joined by smooth moving wave structures. Numerical solutions have been attained to reproduce the different patterns of possible wave structures previously reported in the literature and extended to identify some other new structures and features defining the behaviour of the surface patterns. Copyright © 2006 John Wiley & Sons, Ltd. [source]

On the convergence rate of vanishing viscosity approximations

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2004
Alberto Bressan
Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound ,u(t, ·) , u,(t, ·), = O(1)(1 + t) · |ln ,| on the distance between an exact BV solution u and a viscous approximation u,, letting the viscosity coefficient , , 0. In the proof, starting from u we construct an approximation of the viscous solution u, by taking a mollification u * and inserting viscous shock profiles at the locations of finitely many large shocks for each fixed ,. Error estimates are then obtained by introducing new Lyapunov functionals that control interactions of shock waves in the same family and also interactions of waves in different families. © 2004 Wiley Periodicals, Inc. [source]

Stability of small-amplitude shock profiles of symmetric hyperbolic-parabolic systems

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2004
C. Mascia
Combining pointwise Green's function bounds obtained in a companion paper [36] with earlier, spectral stability results obtained in [16], we establish nonlinear orbital stability of small-amplitude Lax-type viscous shock profiles for the class of dissipative symmetric hyperbolic-parabolic systems identified by Kawashima [20], notably including compressible Navier-Stokes equations and the equations of magnetohydrodynamics, obtaining sharp rates of decay in Lp with respect to small L1 , H3 perturbations, 2 , p , ,. Our analysis extends and somewhat refines the approach introduced in [35] to treat stability of relaxation profiles. © 2004 Wiley Periodicals, Inc. [source]