We prove a BV estimate for scalar conservation laws that generalizes the classical Total Variation Diminishing property. In fact, for any Lipschitz continuous monotone Φ : R→ R, we have that |Φ(u)|TV (R) is nonincreasing in time. We call this property Total Oscillation Diminishing because it is in contradiction with the oscillations observed recently on some numerical computations based on TVD ...

Discretizations of two-fluid flow problems in conservative formulation generally exhibit pressure oscillations. In this work we show that these pressure oscillations are induced by the loss of a pressure-invariance property under discretization, and we introduce a non-oscillatory conservative method for barotropic two-fluid flows. The conservative formulation renders the two-fluid flow problem ...

In this article, we are interested in the simulation of phase transition in compressible flows, with the isothermal Euler system, closed by the van-der-Waals model. We formulate the problem as an hyperbolic system, with a source term located at the interface between liquid and vapour. The numerical scheme is based on [1, 5]. Compared with previous discretizations of the van-der-Waals system, th...

We present a new conservative Cartesian grid embedded boundary method for the solution of the incompressible Navier–Stokes equations in a time-dependent domain. It is a Godunov-projection fractional step scheme in which hyperbolic advection and a variety of implicit and explicit Helmholtz operations are performed on time-stationary domains. The transfer of data from one fixed domain to another ...

This paper is devoted to comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is ut þ ðu uÞx 1⁄4 ðuuxxxÞx, which arises in the context of thin film flow. First we employ implicit schemes and treat both convection and diffusion terms implicitly. Then the convection terms are treated with wellknown explicit schemes, namely Godunov,...

This paper presents the development and testing of time integration scheme for system hydrodynamic equations gas mixture. These take into account phenomena multicomponent diffusion heat transfer. The governing equation is discretized by finite volume approach on three-dimensional unstructured grids. According to algorithm, computation any single step split sequence hyperbolic parabolic stages. ...

We have proposed a new High Resolution Shock Capturing (HRSC) scheme for Special Relativistic Hydrodynamics (SRHD) based on the semidiscrete central Godunov-type schemes and a modified Weighted Essentially Non-oscillatory (WENO) data reconstruction algorithm. This is the first application of the semidiscrete central schemes with high order WENO data reconstruction to the SRHD equations. This me...

We devise a new-class of asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with stiff and non-stiff relaxation source terms governed by a relaxation time ε. As an alternative to classical operator-splitting techniques, the objectives of these schemes are twofold: first, to give accurate numerical solutions for large, small and in-between values of ε and second, to make...

We introduce a new technique for proving a priori error estimates between the entropy weak solution of a scalar conservation law and a finite–difference approximation calculated with the scheme of EngquistOsher, Lax-Friedrichs, or Godunov. This technique is a discrete counterpart of the duality technique introducedbyTadmor [SIAMJ.Numer.Anal. 1991]. The error is related to the consistency error ...