We consider here second-order finite volume methods for onedimensional scalar conservation laws. We give a method to determine a slope reconstruction satisfying all the exact numerical entropy inequalities. It avoids inhomogeneous slope limitations and, at least, gives a convergence rate of ∆x1/2. It is obtained by a theory of second-order entropic projections involving values at the nodes of t...

simula in vivo and to of thi operat muscl from k and S video locom positio during muscl injection of a fixative solution, usually formaldehyde or glutaraldehyde. Muscle fibres are then dissected out and sarcomere length determined microscopically or by light diffraction. James et al. (1995) examined the properties of mouse fast twitch (extensor digitorum longus, EDL) and slow twitch (soleus) mu...

Limiters are nonlinear hybridization techniques that are used to preserve positivity and monotonicity when numerically solving hyperbolic conservation laws. Unfortunately, the original methods suffer from the truncation-error being 1 order accurate at all extrema despite the accuracy of the higher-order method [1, 2, 3, 4]. To remedy this problem, higherorder extensions were proposed that relie...

The multislope concept has been recently introduced in the literature to deal with MUSCL reconstructions on triangular and tetrahedral unstructured meshes in the finite volume cell-centered context. Dedicated scalar slopes are used to compute the interpolations on each face of a given element, in opposition to the monoslope methods in which a unique limited gradient is used. The multislope appr...

A new variable extrapolation formulation for unstructured finite volume codes is developed which closely resembles the MUSCL-scheme used within structured flow solvers. This new formulation is based on information currently available to the unstructured flow solvers, namely the variable information and the gradient information, and as such, it is trivial to implement within most finite volume f...

To simulate accurately and efficiently aerospace-type flows using solely first-order PDE models, new numerical methods may be required to overcome difficulties introduced by the model. We consider a Discontinuous Galerkin (DG) method that has been shown to possess an asymptotic preservation (AP) property for one-dimensional hyperbolic relaxation systems, in an effort to understand the source of...