This paper is the initial investigation into a new Lagrangian cell-centered hydrodynamic scheme that is motivated by the desire for an algorithm that resists mesh imprinting and has reduced complexity. Key attributes of the new approach include multidimensional construction, the use of flux-corrected transport (FCT) to achieve second order accuracy, automatic determination of the mesh motion th...

This talk is dedicated to multi-dimensional numerical simulation of Euler equations for compressible flow problems. To fulfill the conditions of the Lax-Wendroff theorem, it is required that a numerical scheme conserves the mass, momentum and total energy. Associated with the consistency and the increase of the entropy, these conservation properties are sufficient, in 1D, to ensure that a conve...

Numerical schemes for the solution of Euler equations have recently been developed, which involve discretisation internal energy equation, with corrective terms to ensure correct capture shocks, and, more generally, consistency in Lax-Wendroff sense. These may be staggered or colocated, using either structured meshes general simplicial tetrahedral/hexahedral meshes. The time discretization is p...

This work is concerned with the numerical approximation of Cauchy problems for one-dimensional hyperbolic nonconservative systems. Some particular cases of P.D.E. systems which can be considered as particular cases of the nonconservative systems that we study are systems of conservation laws, systems of conservation laws with source term or balance laws and coupled systems of conservation laws ...

in this work, we describe an adjunction between the comma category of set-based monads under the v -powerset monad and the category of associative lax extensions of set-based monads to the category of v -relations. in the process, we give a general construction of the kleisli extension of a monad to the category of v-relations.