An Unstructured Forward-Backward Lagrangian Scheme for Transport Problems

AbstractA multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of spatially distributed agents with strategies, or labels, whose payoff depends also on the current position of the agents. The scheme is Lagrangian, as it traces the evolution of position and labels along characteristics, and is a multi-step scheme, as it develops on the following two stages: First, the distribution of strategies or labels is updated according to a best performance criterion, and then, this is used by the agents to evolve their position. A general convergence result is provided in the space of probability measures. In the special cases of replicator-type systems and reversible Markov chains, variants of the scheme, where the explicit step in the evolution of the labels is replaced by an implicit one, are also considered and convergence results are provided.

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4. Transport Problems

More Surprises in Theoretical Physics ◽

10.1515/9780691214320-006 ◽

1992 ◽

pp. 52-66

Keyword(s):

Transport Problems

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Spectral analysis of the extended linear discontinuous method for one-dimensional monoenergetic discrete ordinates transport problems in non-multiplying media

Annals of Nuclear Energy ◽

10.1016/j.anucene.2021.108172 ◽

2021 ◽

Vol 155 ◽

pp. 108172

Author(s):

Iram B.R. Ortiz ◽

Dany S. Dominguez ◽

Carlos R.G. Hernández ◽

Ricardo C. Barros

Keyword(s):

Spectral Analysis ◽

Discrete Ordinates ◽

One Dimensional ◽

Transport Problems

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Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2020-0029 ◽

2020 ◽

Vol 35 (6) ◽

pp. 355-366

Author(s):

Vladimir V. Shashkin ◽

Gordey S. Goyman

Keyword(s):

Shallow Water ◽

Gravity Waves ◽

Shallow Water Equations ◽

Time Integration ◽

Standard Test ◽

Integration Scheme ◽

Test Problems ◽

Cubed Sphere ◽

Lagrangian Scheme ◽

Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

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Magnetorotational Mechanism of Supernova Explosions - Results of 2D Simulations

Highlights of Astronomy ◽

10.1017/s1539299600021262 ◽

1998 ◽

Vol 11 (1) ◽

pp. 376-376

Author(s):

S.G. Moiseenko

Keyword(s):

Magnetic Field ◽

Equations Of State ◽

Supernova Explosion ◽

Neutrino Energy ◽

Energy Losses ◽

Rotational Momentum ◽

Supernova Explosions ◽

2D Numerical Simulation ◽

Lagrangian Scheme ◽

The Magnetic Field

Results of 2D numerical simulation of the magneto rotational mechanism of a supernova explosion are presented. Simulation has been done for the real equations of state and neutrino energy losses have been taken into account. Simulation has been done on the basis of an Implicit Lagrangian scheme on atriangular grid with grid reconstructuring. It is shown that, due to differential rotation of the star, a toroidal component of the magnetic field appears and grows with time. Rotational momentum transfers outwards as the toroidal component grows with time. With the evolution of the process, part of the envelope of the star is ejected. The amounts of the thrown-off mass and energy are estimated. The results of the simulation could be used as a possible explanation for the supernova explosion picture.

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