In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high order positivity-preserving finite difference WENO methods for the ideal magnetohydrodynamic (MHD) equations. Our schemes, under the constrained transport (CT...

In this paper, we adapt a simple weighted essentially non-oscillatory (WENO) limiter, originally designed for discontinuous Galerkin (DG) schemes on two-dimensional unstructured triangular meshes [35], to the correction procedure via reconstruction (CPR) framework for solving nonlinear hyperbolic conservation laws on two-dimensional unstructured triangular meshes with straight edges or curved e...

In this paper we develop high order positivity-preserving finite volume weighted essentially non-oscillatory (WENO) schemes for solving a hierarchical size-structured population model with nonlinear growth, mortality and reproduction rates. We carefully treat the technical complications in boundary conditions and global integration terms to ensure high order accuracy and positivity-preserving p...

This paper investigates the performances of approximate Riemann solvers (ARSs) for hyperbolic traffic models from family generic second-order flow modeling. Three are selected, including HLL, HLLC, and Rusanov solvers, evaluated comprehensively against model by Zhang (2002) a variant phase-transition Colombo with continuous solution domain. The ARSs investigated using extensive numerical tests,...

In this paper we enhance the well-known fifth order WENO shock-capturing scheme by using deep learning techniques. This fine-tuning of an existing algorithm is implemented training a rather small neural network to modify smoothness indicators in improve numerical results especially at discontinuities. our approach no further post-processing needed ensure consistency method. Moreover, formal acc...

High Mach number astrophysical jets are simulated using a positive scheme, and are compared with WENO-LF simulations. A version of the positive scheme has allowed us to simulate astrophysical jets with radiative cooling up to Mach number 270 with respect to the heavy jet gas, a factor of two times higher than the maximum Mach number attained with the WENO schemes and ten times higher than with ...

We extend the weighted essentially non-oscillatory (WENO) schemes on two dimensional triangular meshes developed in [7] to three dimensions, and construct a third order finite volume WENO scheme on three dimensional tetrahedral meshes. We use the Lax-Friedrichs monotone flux as building blocks, third order reconstructions made from combinations of linear polynomials which are constructed on div...

We present a systematic methodology to develop high order accurate numerical approaches for linear advection problems. These methods are based on evolving parts of the jet of the solution in time, and are thus called jet schemes. Through the tracking of characteristics and the use of suitable Hermite interpolations, high order is achieved in an optimally local fashion, i.e. the update for the d...

In this paper, we propose a class of high-order schemes for solving oneand two-dimensional hyperbolic conservation laws. The methods are formulated in a central finite volume framework on staggered meshes, and they involve Hermite WENO (HWENO) reconstructions in space, and Lax-Wendroff type discretizations or the natural continuous extension of Runge-Kutta methods in time. Compared with central...

Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of firstorder, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill-Whitham-Richards traffic model [4] and a model for the sedimentation of polydisperse suspensions...