We give a proof of the existence of a solution of reconstruction operators used in the $P_N{P}_M$ DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the $P_N{P}_M$ DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several $P_N{P}_M$ DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect...

A space-time formulation for unsteady inviscid compressible flow computations in 2D moving geometries is presented. The governing equations in Arbitrary Lagrangian-Eulerian formulation (ALE) are discretized on two layers of space-time finite elements connecting levels $n$, $n+1/2$ and $n+1$. The solution is approximated with linear variation in space (P1 triangle) combined with linear variation in time. The space-time residual from the lower layer of elements is distributed to the nodes at level...

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=$4 103$.$

In this note, we prove that the $F$-fundamental group scheme is a birational invariant for smooth projective varieties. We prove that the $F$-fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. For elliptic curves, it turns out that the $F$-fundamental group scheme and the Nori fundamental group scheme coincide. We also consider an extension of the Nori fundamental group scheme in positive characteristic using semi-essentially finite vector bundles, and prove...

Intrinsic equations represent promising approach for the description of rotor blade dynamics. They are the system of non-linear partial differential equations. Stability of numeric solution by the finite difference method is described. The stability is studied for various numerical schemes with different methods for the computation of spatial derivatives from time level $n+0.5$ (i.e., mean values of old and new time step) to $n+1$ (i.e., only from new time step). Stable solution was obtained only...

We study the existence of solutions of the nonlinear parabolic problem $\partial u/\partial t-div\left[\right|Du-\Theta \left(u\right){|}^{p-2}(Du-\Theta \left(u\right))]+\alpha \left(u\right)=f$ in ]0,T[ × Ω, $\left(\right|Du-\Theta \left(u\right){|}^{p-2}(Du-\Theta \left(u\right)))·\eta +\gamma \left(u\right)=g$ on ]0,T[ × ∂Ω, u(0,·) = u₀ in Ω, with initial data in L¹. We use a time discretization of the continuous problem by the Euler forward scheme.

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...