Study of numerical error of a Eulerian-Lagrangian scheme in the presence of particle source

2021 ◽  
pp. 107960
Author(s):  
Ryoko Tatsumi ◽  
Kazuo Hoshino ◽  
Akiyoshi Hatayama
Keyword(s):  
Numerical Error ◽  
Particle Source ◽  
Lagrangian Scheme

scholarly journals A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games

2021 ◽  
Author(s):  
Stefano Almi ◽  
Marco Morandotti ◽  
Francesco Solombrino
Keyword(s):  
Mean Field ◽  
Evolutionary Games ◽  
Type Systems ◽  
Convergence Result ◽  
Performance Criterion ◽  
Mean Field Limit ◽  
Spatially Inhomogeneous ◽  
Convergence Results ◽  
Special Cases ◽  
Lagrangian Scheme

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.

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

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.

scholarly journals Integrated quantitative PIXE analysis and EDX spectroscopy using a laser-driven particle source

2021 ◽  
Vol 7 (3) ◽  
pp. eabc8660
Author(s):  
F. Mirani ◽  
A. Maffini ◽  
F. Casamichiela ◽  
A. Pazzaglia ◽  
A. Formenti ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Materials Science ◽  
Quantitative Information ◽  
Pixe Analysis ◽  
Materials Analysis ◽  
Particle Source ◽  
X Ray ◽  
Analysis Techniques ◽  
Sample Structure ◽  
Elemental Characterization

Among the existing elemental characterization techniques, particle-induced x-ray emission (PIXE) and energy-dispersive x-ray (EDX) spectroscopy are two of the most widely used in different scientific and technological fields. Here, we present the first quantitative laser-driven PIXE and laser-driven EDX experimental investigation performed at the Centro de Láseres Pulsados in Salamanca. Thanks to their potential for compactness and portability, laser-driven particle sources are very appealing for materials science applications, especially for materials analysis techniques. We demonstrate the possibility to exploit the x-ray signal produced by the co-irradiation with both electrons and protons to identify the elements in the sample. We show that, using the proton beam only, we can successfully obtain quantitative information about the sample structure through laser-driven PIXE analysis. These results pave the way toward the development of a compact and multifunctional apparatus for the elemental analysis of materials based on a laser-driven particle source.

scholarly journals Magnetorotational Mechanism of Supernova Explosions - Results of 2D Simulations

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.

scholarly journals Numerical and Physical Diffusion: Can Wave Prediction Models Resolve Directional Spread?

2005 ◽  
Vol 22 (7) ◽  
pp. 886-895 ◽  
Author(s):  
F. Ardhuin ◽  
T. H. C. Herbers
Keyword(s):  
Continental Shelf ◽  
Prediction Models ◽  
Spectral Band ◽  
Wave Spectrum ◽  
Single Frequency ◽  
Propagation Time ◽  
Time Step ◽  
Numerical Diffusion ◽  
Wave Prediction ◽  
Lagrangian Scheme

Abstract A new semi-Lagrangian advection scheme called multistep ray advection is proposed for solving the spectral energy balance equation of ocean surface gravity waves. Existing so-called piecewise ray methods advect wave energy over a single time step using “pieces” of ray trajectories, after which the spectrum is updated with source terms representing various physical processes. The generalized scheme presented here allows for an arbitrary number N of advection time steps along the same rays, thus reducing numerical diffusion, and still including source-term variations every time step. Tests are performed for alongshore uniform bottom topography, and the effects of two types of discretizations of the wave spectrum are investigated, a finite-bandwidth representation and a single frequency and direction per spectral band. In the limit of large N, both the accuracy and computation cost of the method increase, approaching a nondiffusive fully Lagrangian scheme. Even for N = 1 the semi-Lagrangian scheme test results show less numerical diffusion than predictions of the commonly used first-order upwind finite-difference scheme. Application to the refraction and shoaling of narrow swell spectra across a continental shelf illustrates the importance of controlling numerical diffusion. Numerical errors in a single-step (Δt = 600 s) scheme implemented on the North Carolina continental shelf (typical swell propagation time across the shelf is about 3 h) are shown to be comparable to the angular diffusion predicted by the wave–bottom Bragg scattering theory, in particular for narrow directional spectra, suggesting that the true directional spread of swell may not always be resolved in existing wave prediction models, because of excessive numerical diffusion. This diffusion is effectively suppressed in cases presented here with a four-step semi-Lagrangian scheme, using the same value of Δt.

Toward a Numerical Error Bar in CFD

1995 ◽  
Vol 117 (1) ◽  
pp. 7-9 ◽  
Author(s):  
George Em Karniadakis
Keyword(s):  
Numerical Error ◽  
Error Bar
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