A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing RungeKutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-d...

The aim of this work is to analyze the use of a number of flux-limiters to simulate numerically the behavior of a homogeneous tubular reactor which exhibits steep moving fronts. The strength and limitations of five different flux-limiters are examined for different test cases. All flux-limiters are found successful in capturing the steep concentration profiles. The simulations show that the min...

This work is devoted to the proposal of a new flux limiter that makes the algebraic flux correction finite element scheme linearity and positivity preserving on general simplicial meshes. Minimal assumptions on the limiter are given in order to guarantee the validity of the discrete maximum principle, and then a precise definition of it is proposed and analyzed. Numerical results for convection...

This work introduces a single-stage, single-step method for the compressible Euler equations that is provably positivitypreserving and can be applied on both Cartesian and unstructured meshes. This method is the first case of a singlestage, single-step method that is simultaneously high-order, positivity-preserving, and operates on unstructured meshes. Time-stepping is accomplished via the Lax-...

A combined IR and visible camera system [G. A. Wurden et al., "A high resolution IR/visible imaging system for the W7-X limiter," Rev. Sci. Instrum. (these proceedings)] and a filterscope system [R. J. Colchin et al., Rev. Sci. Instrum. 74, 2068 (2003)] were implemented together to obtain spectroscopic data of limiter and first wall recycling and impurity sources during Wendelstein 7-X startup ...

Abstract. This paper develops Runge-Kutta PK-based central discontinuous Galerkin (CDG) methods with WENO limiter to the oneand two-dimensional special relativistic hydrodynamical (RHD) equations, K = 1,2,3. Different from the non-central DG methods, the Runge-Kutta CDG methods have to find two approximate solutions defined on mutually dual meshes. For each mesh, the CDG approximate solutions o...

We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to high dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta tim...

Abstract. A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented. In the present work the numerical flux function for space discretization is constructed as a combination of numerical flux function of any entropy ...

We analyse the effect of an Ergodic Magnetic Limiter on the magnetic field line dynamics in the edge of a large aspect-ratio Tokamak. We model the limiter action as an impulsive perturbation and use a peaked-current model for the Tokamak equilibrium field. The theoretical analysis is made through the use of invariant flux functions describing magnetic surfaces. Results are compared with a numer...

New numerical methods have been applied in relativity to obtain a numerical evolution of Einstein equations much more robust and stable. Starting from 3+1 formalism and with the evolution equations written as a FOFCH (first-order flux conservative hyperbolic) system, advanced numerical methods from CFD (computational fluid dynamics) have been successfully applied. A flux limiter mechanism has b...