64,459 research outputs found
Presenting dcpos and dcpo algebras
Dcpos can be presented by preorders of generators and inequational relations expressed as covers. Algebraic operations on the generators (possibly with their results being ideals of generators) can be extended to the dcpo presented, provided the covers are “stable” for the operations. The resulting dcpo algebra has a natural universal characterization and satisfies all the inequational laws satisfied by the generating algebra. Applications include known “coverage theorems” from locale theory
Spectral Volume Method: application to Euler equations and performance appraisal
The compact high-order "Spectral Volume Method" designed for conservation laws on unstructured grids is presented. Its spectral reconstruction is exposed briefly and its applications to the Euler equations are presented through several test cases to assess its accuracy and stability. Comparisons with usual methods such as MUSCL show the superiority of SVM. The SVM method arises as a high-order accurate scheme, geometrically flexible and computationally efficient
Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary
We study nonlinear hyperbolic conservation laws posed on a differential
(n+1)-manifold with boundary referred to as a spacetime, and defined from a
prescribed flux field of n-forms depending on a parameter (the unknown
variable), a class of equations proposed by LeFloch and Okutmustur in 2008. Our
main result is a proof of the convergence of the finite volume method for weak
solutions satisfying suitable entropy inequalities. A main difference with
previous work is that we allow for slices with a boundary and, in addition,
introduce a new formulation of the finite volume method involving the notion of
total flux functions. Under a natural global hyperbolicity condition on the
flux field and the spacetime and by assuming that the spacetime admits a
foliation by compact slices with boundary, we establish an existence and
uniqueness theory for the initial and boundary value problem, and we prove a
contraction property in a geometrically natural L1-type distance.Comment: 32 page
Convergent and conservative schemes for nonclassical solutions based on kinetic relations
We propose a new numerical approach to compute nonclassical solutions to
hyperbolic conservation laws. The class of finite difference schemes presented
here is fully conservative and keep nonclassical shock waves as sharp
interfaces, contrary to standard finite difference schemes. The main challenge
is to achieve, at the discretization level, a consistency property with respect
to a prescribed kinetic relation. The latter is required for the selection of
physically meaningful nonclassical shocks. Our method is based on a
reconstruction technique performed in each computational cell that may contain
a nonclassical shock. To validate this approach, we establish several
consistency and stability properties, and we perform careful numerical
experiments. The convergence of the algorithm toward the physically meaningful
solutions selected by a kinetic relation is demonstrated numerically for
several test cases, including concave-convex as well as convex-concave
flux-functions.Comment: 31 page
Assessment of the Spectral Volume Method on inviscid and viscous flows
The compact high-order "Spectral Volume Method" designed for conservation laws on unstructured grids is presented. Its spectral reconstruction is exposed briefly and its applications to the Euler equations are presented through several test cases to assess its accuracy and stability. Comparisons with classical methods such as MUSCL show the superiority of SVM. The SVM method arises as a high-order accurate scheme, geometrically flexible and computationally efficient
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