We study the stability of a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks. We discretize the Lighthill-Whitham-Richards equations on each road by DG. At traffic junctions, we consider two types of numerical fluxes that are based on Godunov’s numerical flux derived in a previous work of ours. These fluxes are easily constructible for any number of incoming and outgoing roads, respecting the drivers’ preferences. The analysis...

We describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters. In order to solve traffic flows on networks, we construct suitable numerical fluxes at junctions based on preferences of the drivers. Numerical experiment comparing different approaches is presented.

We deal with the simulation of traffic flow on networks. On individual roads we use standard macroscopic traffic models. The discontinuous Galerkin method in space and explicit Euler method in time is used for the numerical solution. We apply limiters to keep the density in an admissible interval as well as prevent spurious oscillations in the numerical solution. To solve traffic networks, we construct suitable numerical fluxes at junctions. Numerical experiments are presented. ...

We deal with a numerical simulation of the inviscid compressible flow with the aid of the combination of the discontinuous Galerkin method (DGM) and backward difference formulae. We recall the mentioned numerical scheme and discuss implementation aspects of DGM, particularly a choice of basis functions and numerical quadratures for integrations. An illustrative numerical example is presented.

In this paper, we propose a new stabilization technique for numerical simulation of incompressible turbulent flow by solving Reynolds-averaged Navier-Stokes equations closed by the SST $k$-$\omega$ turbulence model. The stabilization scheme is constructed such that it is consistent in the sense used in the finite element method, artificial diffusion is added only in the direction of convection and it is based on a purely nonlinear approach. We present numerical results obtained by our in-house...

Let T₁,...,Tₙ be bounded linear operators on a complex Hilbert space H. Then there are compact operators K₁,...,Kₙ ∈ B(H) such that the closure of the joint numerical range of the n-tuple (T₁-K₁,...,Tₙ-Kₙ) equals the joint essential numerical range of (T₁,...,Tₙ). This generalizes the corresponding result for n = 1. We also show that if S ∈ B(H) and n ∈ ℕ then there exists a compact operator K ∈ B(H) such that $\left|\right|(S-K)ⁿ\left|\right|={\left|\right|Sⁿ\left|\right|}_e$. This generalizes results of C. L. Olsen.

In this paper we are concerned with the application of the stabilized finite element method to aero-elastic problems. The main attention is paid to the numerical solution of incompressible viscous two dimensional flow around a flexibly supported solid body. Typical velocities in this case are low enough to assume the air flow being incompressible, on the other hand the Reynolds numbers are very high (${10}^4-{10}^6$). As the neccessary mesh refinement for standard Galerkin approximation is clearly...

This study deals with a numerical solution of a 2D flows of a compressible viscous fluids in a convergent channel for low inlet airflow velocity. Three governing systems – Full system, Adiabatic system, Iso-energetic system$basedontheNavier-Stokesequationsforlaminarflowaretested.Thenumericalsolutionisrealizedbyfinitevolumemethodandthepredictor-correctorMacCormackschemewithJamesonartificialviscosityusingagridofquadrilateralcells.TheunsteadygridofquadrilateralcellsisconsideredintheformofconservationlawsusingArbitraryLagrangian-Eulerianmethod.Thenumericalresults,acquiredfromadevelopedprogram,arepresentedforinletvelocity$u=4.12 ms-1$andReynoldsnumberRe=$4 103$.$

This paper deals with the construction of numerical solution of the Black-Scholes (B-S) type equation modeling option pricing with variable yield discrete dividend payment at time $t_d$. Firstly the shifted delta generalized function $\delta (t-t_d)$ appearing in the B-S equation is approximated by an appropriate sequence of nice ordinary functions. Then a semidiscretization technique applied on the underlying asset is used to construct a numerical solution. The limit of this numerical solution is independent...