Stochastic Richardson Extrapolation Based Numerical Error Estimation for Kinetic Plasma Simulations

Radtke, Gregg Arthur; Cartwright, Keith; Musson, Lawrence

doi:10.2172/1504853

Cited by 5 publications

(11 citation statements)

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“…In some Monte Carlo codes, such as particle‐in‐cell simulations, the particle trajectories are not independent. The means of demonstrating that such a simulation converges to an expected solution are not straightforward . Moreover, the method of manufactured solutions is not so easy to apply either.…”

Section: Verificationmentioning

confidence: 99%

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Computer Simulation in Low‐Temperature Plasma Physics: Future Challenges

Turner

2016

Plasma Processes & Polymers

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Computer simulations can be carried out with various aims. Perhaps the most challenging is prediction under conditions where experiments are difficult or inaccessible, especially when failure to predict adequately may have unhappy consequences. There is, probably, not much confidence at present in the capability of low‐temperature plasma physics simulations in such a context. Other fields have attempted to meet this challenge using a collection of techniques collectively known as “Verification and Validation,” or “V&V.” These are methods for enhancing confidence in the correctness and fidelity of computer simulations. This paper surveys these techniques and discusses their application to improvements of simulation capability in low‐temperature plasma physics.

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Section: Verificationmentioning

confidence: 99%

“…The means of demonstrating that such a simulation converges to an expected solution are not straightforward. [27] Moreover, the method of manufactured solutions is not so easy to apply either. This is because implementing an arbitrary source term is not simple.…”

Section: Monte Carlo Codesmentioning

confidence: 99%

Computer Simulation in Low‐Temperature Plasma Physics: Future Challenges

Turner

2016

Plasma Processes & Polymers

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“…Such a solution can not only verify the numerical methods used in benchmarked codes, but can also be used to obtain unprecedented information on the accuracy of different numerical methods or implementation schemes: without having to establish and run additional benchmark cases between multiple, independent codes. Generally, one can distinguish between verification solutions which are true analytical solutions of the underlying fundamental equations (or more commonly a simplified version thereof) [12][13][14], and solutions that have been 'manufactured' by modifying the fundamental equations themselves [15][16][17][18]. This latter approach is typically referred to as the method of manufactured solutions (MMS) and can be a useful strategy for generating verification solutions when a true analytical solution is not possible, or not available.…”

Section: Introductionmentioning

confidence: 99%

“…Access to true analytical solutions for kinetic simulations is particularly sparse given the complexity of the Vlasov and Boltzmann equations. One such solution however, is space-charge limited (SCL) charged particle flow through a planar diode which has been used to verify several electrostatic PIC simulation codes [7,13,19].…”

Section: Introductionmentioning

confidence: 99%

“…We treat the simple, but important, problem of current transmission between two electrodes, and derive a theoretical solution that completely describes the system. In contrast to the existing SCL verification solution used in [7,13,19], the present complimentary solution is completely analytical and does not require the numerical evaluation of any integrals (which may add additional errors during verification if care is not taken), provides expressions for the spatial variation of all quantities (including the density, velocity, electric field, and potential), is applicable to both fluid and kinetic simulations, represents an entire family of solutions, and allows the applied voltage across the electrodes to be non-zero (hence providing further possibilities for simulation stress testing).…”

Section: Introductionmentioning

confidence: 99%

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Space-charge affected current flow: an analytical verification solution for kinetic and fluid simulation models

Lafleur¹

2022

Plasma Sources Sci. Technol.

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Veriﬁcation of numerical simulations is an important step in code development as it demonstrates the correctness of the code in solving the underlying physical model. Analytical solutions represent a strong tool in code veriﬁcation, but due to the complexity of the fundamental equations, such solutions are often not always available. This is particularly true in the case of kinetic models. Here we present a family of fully analytical solutions describing current transmission between two electrodes and which apply to both ﬂuid, and kinetic, descriptions of the system. The solutions account for the ﬁnite initial particle injection velocity and are valid for all injection currents between zero and the maximum at the space-charge limit. In addition to determining this space-charge limited current, spatial proﬁles of all physical quantities (such as the particle density and velocity) are also obtained at all injection currents. This provides a means to not only verify ﬂuid and kinetic simulations, but also to assess the error and accuracy of the numerical simulation methods and parameters used. The analytical solutions extend the classical Child-Langmuir law (which only applies to the maximum transmissible current and an initial injection velocity equal to zero), and provide new insight into space-charge affected current flow.

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Verification of particle-in-cell simulations with Monte Carlo collisions

Turner

2016

Plasma Sources Sci. Technol.

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Abstract. Widespread recent interest in techniques for demonstrating that computer simulation programs are correct ("verification") has been motivated by evidence that traditional development and testing procedures are disturbingly ineffective.Reproducing an exact solution of the relevant model equations is generally accepted as the strongest available verification procedure, but this technique depends on the availability of suitable exact solutions. In this paper we consider verification of a particle-in-cell simulation with Monte Carlo collisions. We know of no exact solutions that simultaneously exercise all of the functions of this code. However, we show here that there can be found in the literature a number of non-trivial exact solutions, each of which exercises a substantial subset of these functions, and which in combination exercise all of the functions of the code. That the code is able to reproduce these solutions is correctness evidence of a stronger kind than has hitherto been elucidated.

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Stochastic Richardson Extrapolation Based Numerical Error Estimation for Kinetic Plasma Simulations

Cited by 5 publications

References 0 publications

Computer Simulation in Low‐Temperature Plasma Physics: Future Challenges

Computer Simulation in Low‐Temperature Plasma Physics: Future Challenges

Space-charge affected current flow: an analytical verification solution for kinetic and fluid simulation models

Verification of particle-in-cell simulations with Monte Carlo collisions

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