Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation.
Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation.
Numerical approximation of the inviscid 3D primitive equations in a limited domain
A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.
Numerical approximation of the inviscid 3D primitive equations in a limited domain
A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.
Numerical Modeling of the Stream Dynamics for River Channels with Complex Spatial Configuration
Mathematical modeling provides a particularly important tool for studying the stream runoff formation processes, and its role is enhanced in the case of a sparse, obsolete monitoring network characteristic of most regions of Siberia. When analyzing spatio-temporal regularities of the water and sediment runoff in river systems, serious problems are caused by lack of the basic hydrological model capable of handling real-time data of hydrological measurements. Calculations of unsteady flows in stream...
Numerical simulation of internal tides in the Strait of Gibraltar.
Presentamos un modelo numérico unidimensional para flujos bicapa que se ha desarrollado para la simulación de flujos a través de canales con geometría irregular tanto en anchura como en profundidad. Este modelo se utiliza para el estudio y simulación de las mareas internas que tienen lugar en el Estrecho de Gibraltar. En primer lugar presentaremos las ecuaciones del modelo y el esquema numérico que se usa para su resolución. A continuación evaluaremos el buen hacer del modelo numérico comparando...
Numerical studies of groundwater flow problems with a singularity
The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock...