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Toro, E.F. (author), Dumbser, M. (author), Titarev, V.A. (author), Käser, M. (author)The corner stone of arbitrary high order schemes (ADER schemes) is the solution of the derivative Riemann problem at the element interfaces, a generalization of the classical Riemann problem first used by Godunov in 1959 to construct a first-order upwind numerical method for hyperbolic systems. The derivative Riemann problem extends the possible...conference paper 2006
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Titarev, V.A. (author), Romenski, E.I. (author), Toro, E.F. (author)Numerical methods for solving non-linear systems of hyperbolic conservation laws via finite volume methods or discontinuous Galerkin finite element methods require, as the building block, a monotone numerical flux. The simplest approach for providing a monotone numerical utilizes a symmetric stencil and does not explicitly make use of wave...conference paper 2006
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Hidalgo, A. (author), Toro, E.F. (author), Conde, C. (author)Nonlinear acoustic waves have many applications in very different fields of industry. The problem considered in this work consists of predicting the behaviour of gas filling a one dimensional tube when suffering the action of very high frequency waves. The numerical technique applied to solve this problem is a third order finite volume method...conference paper 2006
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Castro, C.E. (author), Toro, E.F. (author)Compressible multiphase models have been studied for a long time inspired on different applications in diverse engineering areas. Solutions for these equations are not simple and researcher have spent much time trying to bring answers. The possibility to properly solve these equations and perform real simulations represent a very ambitious goal....conference paper 2006
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Vignoli, G. (author), Toro, E.F. (author), Titarev, V. (author)In this paper we develop one dimensional non-linear ADER schemes for the shallow water system with source terms. In contrast to conventional schemes we adopt a formulation given in terms of the free surface elevation and water discharge. Data reconstruction is performed using ENO polynomials both for the conservative variables and for the bottom...conference paper 2006
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Titarev, V.A. (author), Toro, E.F. (author)In this paper we generalizew the semi-analytical method16 for solving the Derivative Riemann Problem to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection schemes. We provide numerical examples for two...conference paper 2006
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Toro, E.F. (author)Very simple linearisations for the solution to the Riemann problem for the time-dependent and for the steady supersonic Euler equations are presented. When used locally in conjunction with Godunov-type methods, computing savings by a factor of about four, relative to the use of exact Riemann solvers, can be achieved. For severe flow regimes...report 1991
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Toro, E.F. (author)Paper presented at the 9th GAMM Conference on Numerical Methods of Fluid Mechanics, Laussane, Switzerland, September 1991. We present Numerical Viscosity Functions, or NVFs, for use with Riemann-problem based shock-capturing methods as applied to viscous flows. In particular, viscous flux limiters are derived. The analysis pertain to a linear...report 1991
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Toro, E.F. (author)Three topics on modern shock capturing methods for the time-dependent Euler equations of Gas Djméimics are addressed. First we present the Weighted Average Flux Method (or WAF), one of several Riemêinn-problem based shock capturing methods. Then we deal with the Riemann problem. We present an efficient exact Riemann solver, a robust non...report 1991
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Toro, E.F. (author)The time-dependent Euler equations of Gas Dynamics are a set of non-linear hyperbolic conservation laws that admit discontinuous solutions (e.g.shocks). In this paper we are concerned with Riemann problem based numerical methods for solving the general initial-value problem for these equations. We present an approximate, lineeu'ised Riemann...report 1991
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Clarke, J.F. (author), Karni, S. (author), Quirk, J.J. (author), Simmonds, L.G. (author), Toro, E.F. (author)We are concerned with theoretical modelling of unsteady, two-dimensional detonation waves in high energy solids. A mathematical model and a numerical method to solve the associated hyperbolic system of equations are presented. The model consists of the Euler equations augmented bby extra conservation laws and source terms to accoxint for...report 1990
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Toro, E.F. (author)An exact Riemann solver for the shallow water equations along with several approximate Riemann solvers are presented. These solutions are used locally to compute numerically the global solution of the general initial boundary value problem for the shallow water equations. The numerical method used is the weighted average flux method (WAF)...report 1990
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Toro, E.F. (author)Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.report 1990
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Toro, E.F. (author)Oscillation-free versions of the weighted average flux (WAF) method for the model equation ut aux = 0 are presented. Two approaches are discussed in detail namely. Courant Number amplification and flux, or weight, limiting. Extended TVD regions are derived and amplifying/limiting functions are constructed. Numerical experiments on and ul aux = 0...report 1989
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Toro, E.F. (author)The Riemann problem for the unsteady, one dimensional Euler equations together with the constant-covolume equation of state is solved exactly. The solution is then applied to the Random Choice Method to solve the general initialboundary value problem for the Euler equations. The iterative procedure to find p*, the pressure between the acoustic...report 1987
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Toro, E.F. (author)A practical description of the Random Choice Method (RCM) on non-staggered grids is presented. The original idea appears to be due to Colella (1982). The approach is much simpler than the staggered grid version of RCM, which is the one traditionally used. It also offers a number of advantages with regards to use of non-regular meshes in space...report 1987
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Clarke, J.F. (author), Roe, P.L. (author), Simmonds, L.G. (author), Toro, E.F. (author)Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.report 1987
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Toro, E.F. (author)A new computational method for hyperbolic conservation laws in one space dimension is presented. This technique is based on the Random Choice Method (RCM). The first step is exactly as in RCM with secondary grid, whereby intercell values at half time levels are provided. The second step completes the solution at time level n 1 via a finite...report 1986
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Toro, E.F. (author)Numerical computations of non-linear gravity uaues are presented and the effects of mesh variations on the results are discussed. Waves are regarded as tujo-parameter families (X,A) of arbitrary discharge Q, and computations are carried out using a new Kantorovich algorithm. Mesh effects are to a large extent, dependent on the particular uiave...report 1985
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Toro, E.F. (author)Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.report 1984