Regularized Equations for Numerical Simulation of Flows in the Two-Layer Shallow Water Approximation

Application of Graphics Processing Units for Self-Consistent Modelling of Shallow Water Dynamics and Sediment Transport

“…It is widely accepted that a consistent description of the dynamics of the surface water flow and sediment transport requires the use of multilayer models in the shallow water approximation [17][18][19]. In this approach, the Saint-Venant equations should be written in the form of the Exner equation [7,12,20] which allows simulating the dynamics of soil erosion and sediment movement due to fluid flow.…”

Improving the Efficiency of Protection of the Forest Fire Machine against Forest Fires with the Help of Composite Materials

“…In the construction of the model takes into account the heat transfer in laminar motion of hot gases near the surface of the CM, the transfer of heat due to radiation, as well as the thermal conductivity inside the layer of CM and the enclosure of the cabin of the fire truck. To describe the processes under consideration, partial differential equations are used, namely, the Navier-Stokes equations, the energy equation, the radiation transfer equation in a transparent medium and the thermal conductivity equation for solids [19][20][21]. The finite volume method is used to solve the model numerically (Fig.…”

On Conditions for L2-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations

“…These methods are widely used for numerical solution of various applied problems. In the barotropic case, gas dynamics systems of equations with such regularizations were introduced and studied in [10][11][12][13], and their numerous applications to computer simulation were given for various 1D and 2D shallow water models [14][15][16][17][18][19], some 2D astrophysical problems [20] and the 2D and 3D compressible Navier-Stokes-Cahn-Hilliard models [21][22][23], etc. Despite of a lot of applications, almost nothing was known until recent years on rigorous theoretical conditions for stability of schemes with the QGD and QHD regularizations thus leading to additional time-consuming preliminary numerical experiments in order to choose the adequate parameters of schemes allowing to use larger values of ∆t.…”