Effect of altitude is discussed in the unsteady separation of multi stage rockets. Axisymmetric, unsteady and turbulent Navier stokes equations are solved numerically. The governing equations are split into a hyperbolic inviscid part and a parabolic diffusion part. The hyperbolic part is solved by an explicit second-order time and space of Godunov-type scheme. Moving mesh and moving boundary al...

A two-phase model of heterogeneous explosives, due to Baer and Nunziato, is examined computationally by a new numerical approach that is a modification of the standard Godunov scheme. The approach generates well-resolved and accurate solutions economically, and treats rationally the nozzling terms that render the otherwise hyperbolic model incapable of a conservative representation. A broad ran...

The Euler-Maxwell equations as a hydrodynamic model of charge transport of semiconductors in an electromagnetic field are studied. The global approximate solutions to the initial-boundary value problem are constructed by the fractional Godunov scheme. The uniform bound and H−1 compactness are proved. The approximate solutions are shown convergent by weak convergence methods. Then, with some new...

We investigate the application of weighted essentially nonoscillatory (WENO) reconstructions to a class of semi-Lagrangian schemes for first order time-dependent Hamilton–Jacobi equations. In particular, we derive a general form of the scheme, study sufficient conditions for its convergence with high-order reconstructions, and perform numerical tests to study its efficiency. In addition, we pro...

We introduce a new homogenized hyperbolic (multi-class) tra c ow model which allows to take into account the behaviors of di erent type of vehicles (cars, trucks, buses, etc.) and drivers. We discretize the starting Lagrangian system introduced below with a Godunov scheme, and we let the mesh size h in (x, t) go to 0: the typical length (of a vehicle) and time vanish. Therefore, the variables h...

A posteriori L error estimates (in the sense of [12, 23]) are derived for both well-balanced (WB) and fractional-step (FS) numerical approximations of the unique weak solution of the Cauchy problem for the 1D semilinear damped wave equation. For setting up the WB algorithm, we proceed by rewriting it under the form of an elementary 2 × 2 system which linear convective structure allows to reduce...

This paper considers the Riemann problem and an associated Godunov method for a model of compressible two-phase flow. The model is a reduced form of the wellknown Baer-Nunziato model which describes the behavior of granular explosives. In the analysis presented here, we focus on the effect of non-conservative nozzling terms in the two-phase model and omit source terms representing the exchange ...

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are considered as graphs composed by arcs that meet at some junctions. The crucial point is represented by junctions, where interactions occurr and the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative met...

Robust and accurate schemes are designed to simulate the coupling between subsurface and overland flows. The coupling conditions at the interface enforce the continuity of both the normal flux and the pressure. Richards’ equation governing the subsurface flow is discretized using a Backward Differentiation Formula and a symmetric interior penalty Discontinuous Galerkin method. The kinematic wav...

This paper introduces the use of moving least-squares (MLS) approximations for the development of high-order finite volume discretizations on unstructured grids. The field variables and their successive derivatives can be accurately reconstructed using this mesh-free technique in a general nodal arrangement. The methodology proposed is used in the construction of two numerical schemes for the s...