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Numerical Modeling of the Stream Dynamics for River Channels with Complex Spatial Configuration

V. A. Shlychkov (2009)

Mathematical Modelling of Natural Phenomena

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.

Manuel J. Castro, José Manuel González Vida, Jorge Macías, M.L. Muñoz, Carlos Parés, José Antonio García Rodríguez, Carlos Vázquez Cendón (2002)

RACSAM

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 simulation of the motion of a three-dimensional glacier

Marco Picasso, Jacques Rappaz, Adrian Reist (2008)

Annales mathématiques Blaise Pascal

The motion of a three-dimensional glacier is considered. Ice is modeled as an incompressible non-Newtonian fluid. At each time step, given the shape of the glacier, a nonlinear elliptic system has to be solved in order to obtain the two components of the horizontal velocity field. Then, the shape of the glacier is updated by solving a transport equation. Finite element techniques are used to compute the velocity field and to solve the transport equation. Numerical results are compared to experiments...

Numerical simulations of glacial rebound using preconditioned iterative solution methods

Erik Bängtsson, Maya Neytcheva (2005)

Applications of Mathematics

This paper discusses finite element discretization and preconditioning strategies for the iterative solution of nonsymmetric indefinite linear algebraic systems of equations arising in modelling of glacial rebound processes. Some numerical experiments for the purely elastic model setting are provided. Comparisons of the performance of the iterative solution method with a direct solution method are included as well.

Numerical studies of groundwater flow problems with a singularity

Hokr, Milan, Balvín, Aleš (2017)

Programs and Algorithms of Numerical Mathematics

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...

On a stochastic parabolic PDE arising in climatology.

Gregorio Díaz, Jesús Ildefonso Díaz (2002)

RACSAM

Estudiamos la existencia y unicidad de soluciones de una ecuación estocástica en derivadas parciales de tipo parabólico propuesta por R. North y R. F. Cahalan en 1982 para la modelización de variabilidad no determinista (como es el caso, por ejemplo, de la acción de volcanes) en el marco de los modelos de balance de energía. El punto más delicado se refiere a la unicidad de soluciones debido a la presencia de un grafo multívoco β en el término de la derecha de la ecuación. En contraste con el caso...

On a type of Signorini problem without friction in linear thermoelasticity

Jiří Nedoma (1983)

Aplikace matematiky

In the paper the Signorini problem without friction in the linear thermoelasticity for the steady-state case is investigated. The problem discussed is the model geodynamical problem, physical analysis of which is based on the plate tectonic hypothesis and the theory of thermoelasticity. The existence and unicity of the solution of the Signorini problem without friction for the steady-state case in the linear thermoelasticity as well as its finite element approximation is proved. It is known that...

On caustics associated with Rossby waves

Arthur D. Gorman (1996)

Applications of Mathematics

Rossby wave equations characterize a class of wave phenomena occurring in geophysical fluid dynamics. One technique useful in the analysis of these waves is the geometrical optics, or multi-dimensional WKB technique. Near caustics, e.g., in critical regions, this technique does not apply. A related technique that does apply near caustics is the Lagrange Manifold Formalism. Here we apply the Lagrange Manifold Formalism to study Rossby waves near caustics.

On dynamics of fluids in meteorology

Lukáš Poul (2008)

Open Mathematics

We consider the full Navier-Stokes-Fourier system of equations on an unbounded domain with prescribed nonvanishing boundary conditions for the density and temperature at infinity. The topic of this article continues author’s previous works on existence of the Navier-Stokes-Fourier system on nonsmooth domains. The procedure deeply relies on the techniques developed by Feireisl and others in the series of works on compressible, viscous and heat conducting fluids.

On inversions of van der Grinten projections

Tomáš Bayer, Milada Kočandrlová (2021)

Applications of Mathematics

Approximately 150 map projections are known, but the inverse forms have been published for only two-thirds of them. This paper focuses on finding the inverse forms of van der Grinten projections I--IV, both by non-linear partial differential equations and by the straightforward inverse of their projection equations. Taking into account the particular cases, new derivations of coordinate functions are also presented. Both the direct and inverse equations have the analytic form, are easy to implement...

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