This paper discusses several aspects related to the consistency and stability of the discrete adjoints of upwind numerical schemes. First and third order upwind discretizations of the one-dimensional advection equation are considered in both the finite difference and finite volume formulations. We show that the discrete adjoints may lose consistency and stability near the points where upwinding...

In the field of strong-stability-preserving time discretizations, a number of researchers have considered using both upwind and downwind approximations for the same derivative, in order to guarantee that some strong stability condition will be preserved. The cost of computing both the upwind and downwind operator has always been assumed to be double that of computing only one of the two. Howeve...

The nsmb code (Navier-Stokes Multi-Block) solves the fully coupled system of equations simultaneously using a cell-centered finitevolume approach. This note assesses the sensitivity to some turbulence models and numerical schemes implemented in nsmb when computing two test cases in standard mode, that is, without tuning the code to these two cases. The cases are 1. subsonic flow around the ms(1...

High-performance liquid chromatography (HPLC) is a dynamic separation process with lot of parameters having different roles. The equilibrium-dispersive model relevant for simulating HPLC because it relatively simple and suitable high-efficiency processes. partial differential equation was simulated in many methods such as semi-analytical methods, finite element difference methods. Many studies ...

The standard construction of upwind diierence schemes for hyper-bolic systems of conservation laws requires the full eigensystem of the Jacobian matrix. This system is used to deene the transformation into and out of the characteristic scalar elds, where upwind diierencing is meaningful. When the Jacobian has a repeated eigenvalue, the associated normalized eigenvectors are not uniquely determi...

We analyze one-sided or upwind finite difference approximations to hyperbolic partial differential equations and, in particular, nonlinear conservation laws. Second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions. We show that no such stable approximation of order higher than two is possible. These one-sided ...

This chapter presents a constructive derivation of HDG methods for convection-diffusion-reaction equation using the Rankine-Hugoniot condition. This is possible due to the fact that, in the first order form, convection-diffusion-reaction equation is a hyperbolic system. As such it can be discretized using the standard upwind DG method. The key is to realize that the Rankine-Hugoniot condition n...