High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations require positivity of thermodynamic quantities in order to guarantee their well-posedness. In this work, we introduce a limiting strategy discretizations constructed by blending high solutions with low positivity-preserving discretization. The proposed discretization is semi-discretel...

We propose an algorithm for the global optimization of continuous minimax problems involving polynomials. The method can be described as a discretization approach to the well known semi-infinite formulation of the problem. We 1 Financial support of EPSRC Grant GR/T02560/01 gratefully acknowledged. 2 Research Associate, Department of Computing, Imperial College, London, UK. 3 Professor, Departme...

The almost automorphic solution is a generalization of the almost periodic solution. In this paper, the almost automorphic solutions of Cohen-Grossberg neural networks with delays are considered. Using the semi-discretization method and the contraction mapping principle, some sufficient conditions are obtained to ensure the existence and the uniqueness of almost automorphic solutions to Cohen-G...

A new high order Arakawa-like method for the incompressible vorticity equation in two-dimensions has been developed. Mimetic properties such as skewsymmetry, energy and enstrophy conservations for the semi-discretization are proved for periodic problems using arbitrary high order summation-by-parts operators. Numerical simulations corroborate the theoretical findings.

The recently developed TECNO schemes for hyperbolic conservation laws are designed to be high-order accurate and entropy stable, but are, as of yet, only semi-discrete. We perform an explicit discretization of the temporal derivative to obtain a fully discrete scheme, and derive a non-strict CFL condition that ensures global entropy stability. The scheme is tested in a series of numerical exper...

We investigate in this paper the problem of discrete ray-tracing. The incorrect intersection phenomena are shown. The need of a specific discretization is discussed according to these problems. We propose a restricted use of a semi-discrete ray-tracer which avoid some problems that arose with discrete ray-tracing.

Models for multiphase-multicomponent flow in porous media are described in systems of PDEs. Solving them using finite difference discretization method can be of three ways; explicit, semi-implicit, and fully implicit. In this study, we present the implementation of an adaptive Newton-Raphson method in the context of IMPECS (Implicit Pressures Explicit Concentrations and Saturations) method of s...