GAVRILYUK , Sergey

The conduit equation is a dispersive non-integrable scalar equation modeling the flow of a low-viscous buoyant fluid embedded in a highly viscous fluid matrix. This equation can be written in a special form reminiscent of the famous Godunov form proposed in 1961 for the Euler equations of compressible fluids. We propose a hyperbolic...

In this paper we propose a fluctuation splitting finite volume scheme for a non-conservative modeling of shear shallow water flow (SSWF). This model was originally proposed by Teshukov (2007) in [14] and was extended to include modeling of friction by Gavrilyuk et al. (2018) in [7]. The directional splitting scheme proposed by Gavrilyuk et al....

We develop and implement a finite volume method based on a conservative approach for the hyperbolic non-conservative system of the shear shallow water model. This model is a generalization of the shallow water model to include the effects of shear, which are ignored in the standard shallow water model. The existing path conservative scheme is...

We show that, contrary to popular belief, lower order dispersive regularization of hyperbolic systems does not exclude the development of the localized shock-like transition fronts. To guide the numerical search of such solutions, we generalize Rankine-Hugoniot relations to cover the case of higher order dispersive ...

We show that, contrary to popular belief, lower order dispersive regularization of hyperbolic systems does not exclude the development of the localized shock-like transition fronts. To guide the numerical search of such solutions, we generalize Rankine–Hugoniot relations to cover the case of higher order dispersive discontinuities and study...

We show that, contrary to popular belief, lower order dispersive regularization of hyperbolic systems does not exclude the development of the localized shock-like transition fronts. To guide the numerical search of such solutions, we generalize Rankine-Hugoniot relations to cover the case of higher order dispersive ...

The formation of a periodic roll-wave train in a long channel is studied for two sets of experimental parameters (noted as Case 1 and Case 2) corresponding to Brock's experiments [3], [4]. In both cases, a formed free surface profile was found in a very good agreement with the experimental results. Mathematical properties of the model were also...