A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

doi:10.1016/j.jcp.2016.03.070

Title: A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

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Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.

Authors:

Chacon, L. ^[1] ; Chen, G. ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: 2016-04-19

Report Number(s):: LA-UR-15-27639
Journal ID: ISSN 0021-9991

Grant/Contract Number:: AC52-06NA25396

Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 316; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Research Org:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org:: USDOE

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Mathematics; Magnetic Fusion Energy

OSTI Identifier:: 1255248

Alternate Identifier(s):: OSTI ID: 1348010


                    Chacon, L., and Chen, G.. A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions.  United States: N. p.,  
        Web.  doi:10.1016/j.jcp.2016.03.070.

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                    Chacon, L., & Chen, G.. A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions.  United States.  doi:10.1016/j.jcp.2016.03.070.

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                    Chacon, L., and Chen, G.. 2016.  
        "A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions".  United States.  
        doi:10.1016/j.jcp.2016.03.070.  https://www.osti.gov/servlets/purl/1255248.

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@article{osti_1255248,

  title        = {A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions},

  author       = {Chacon, L. and Chen, G.},

  abstractNote = {Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.},

  doi          = {10.1016/j.jcp.2016.03.070},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 316,

  place        = {United States},

  year         = {2016},

  month        = {4}

}

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10.1016/j.jcp.2016.03.070
https://doi.org/10.1016/j.jcp.2016.03.070

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