Second-order well-balanced Lagrange-projection schemes for blood flow equations

High-order Well-balanced Schemes

Efficient well-balanced hydrostatic upwind schemes for shallow-water equations

The proposed work concerns the numerical approximations of the shallow-water equations with varying topography. The main objective is to introduce an easy and systematic technique to enforce the well-balance property and to make the scheme able to deal with dry areas. To access such an issue, the derived numerical method is obtained by involving the free surface instead of the water height and ...

A Second Order Well-Balanced Finite Volume Scheme for Euler Equations with Gravity

We present a well-balanced, second order, Godunov-type finite volume scheme for compressible Euler equations with gravity. By construction, the scheme admits a discrete stationary solution which is a second order accurate approximation to the exact stationary solution. Such a scheme is useful for problems involving complex equations of state and/or hydrostatic solutions which are not known in c...

On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes

We present in this paper a rigorous error analysis of several projection schemes for the approximation of the unsteady incompressible NavierStokes equations. The error analysis is accomplished by interpreting the respective projection schemes as second-order time discretizations of a perturbed system which approximates the Navier-Stokes equations. Numerical results in agreement with the error a...

High-order well-balanced schemes and applications to non-equilibrium flow

The appearance of the source terms in modeling non-equilibrium flow problems containing finite-rate chemistry or combustion poses additional numerical difficulties beyond that for solving non-reacting flows. A well-balanced scheme, which can preserve certain non-trivial steady state solutions exactly, may help minimize some of these difficulties. In this paper, a simple one-dimensional non-equi...