Biot-Savart Law

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Makoto Tsubota - One of the best experts on this subject based on the ideXlab platform.

  • steady state counterflow quantum turbulence simulation of vortex filaments using the full biot savart Law
    Physical Review B, 2010
    Co-Authors: Hiroyuki Adachi, Shoji Fujiyama, Makoto Tsubota
    Abstract:

    We perform a numerical simulation of quantum turbulence produced by thermal counterflow in superfluid $^{4}\text{H}\text{e}$ by using the vortex filament model with the full Biot-Savart Law. The pioneering work of Schwarz has two shortcomings: it neglects the nonlocal terms of the Biot-Savart integral [known as the localized induction approximation (LIA)] and it employs an unphysical mixing procedure to sustain the statistically steady state of turbulence. We have succeeded in generating the statistically steady state under periodic boundary conditions without using the LIA or the mixing procedure. This state exhibits the characteristic relation $L={\ensuremath{\gamma}}^{2}{v}_{ns}^{2}$ between the line-length density $L$ and the counterflow relative velocity ${v}_{ns}$ and there is quantitative agreement between the coefficient $\ensuremath{\gamma}$ and some measured values. The parameter $\ensuremath{\gamma}$ and some anisotropy parameters are calculated as functions of temperature and the counterflow relative velocity. The numerical results obtained using the full Biot-Savart Law are compared with those obtained using the LIA. The LIA calculation constructs a layered structure of vortices and does not proceed to a turbulent state but rather to another anisotropic vortex state; thus, the LIA is not suitable for simulations of turbulence.

  • energy spectrum of superfluid turbulence with no normal fluid component
    Physical Review Letters, 2002
    Co-Authors: Tsunehiko Araki, Makoto Tsubota, Sergey K Nemirovskii
    Abstract:

    : The energy of superfluid turbulence without the normal fluid is studied numerically under the vortex filament model. Time evolution of the Taylor-Green vortex is calculated under the full nonlocal Biot-Savart Law. It is shown that for k<2pi/l the energy spectrum is very similar to the Kolmogorov's -5/3 Law which is the most important statistical property of the conventional turbulence, where k is the wave number of the Fourier component of the velocity field and l is the average intervortex spacing. The vortex length distribution converges to a scaling property reflecting the self-similarity of the tangle.

A V Gorshkov - One of the best experts on this subject based on the ideXlab platform.

  • Associated Weber–Orr Transform, Biot–Savart Law and Explicit Form of the Solution of 2D Stokes System in Exterior of the Disc
    Journal of Mathematical Fluid Mechanics, 2019
    Co-Authors: A V Gorshkov
    Abstract:

    In this article we derive the explicit formula for the solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity \(\mathbf {v}_\infty \) at infinity. It turned out it is the first application of the associated Weber–Orr transform to mathematical physics in comparison to classical Weber–Orr transform which is used in many researches. From no-slip condition for velocity field we will obtain Robin-type boundary condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber–Orr transform. Also the explicit formula of Biot–Savart Law in polar coordinates will be given.

  • associated weber orr transform biot savart Law and explicit form of the solution of 2d stokes system in exterior of the disc
    Journal of Mathematical Fluid Mechanics, 2019
    Co-Authors: A V Gorshkov
    Abstract:

    In this article we derive the explicit formula for the solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity \(\mathbf {v}_\infty \) at infinity. It turned out it is the first application of the associated Weber–Orr transform to mathematical physics in comparison to classical Weber–Orr transform which is used in many researches. From no-slip condition for velocity field we will obtain Robin-type boundary condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber–Orr transform. Also the explicit formula of Biot–Savart Law in polar coordinates will be given.

  • associated weber orr transform biot savart Law and explicit solution of 2d stokes system in exterior of the disc
    arXiv: Analysis of PDEs, 2019
    Co-Authors: A V Gorshkov
    Abstract:

    In this article we derive the explicit solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity $\mathbf{v}_\infty$ at infinity. It turned out it is the first application of the associated Weber-Orr transform to mathematical physics in comparison to classical Weber-Orr transform which is used in many researches. From no-slip condition for velocity field we will obtain Robin-type boundary condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber-Orr transform. Also the explicit formula of Biot-Savart Law in polar coordinates will be given.

Sergey K Nemirovskii - One of the best experts on this subject based on the ideXlab platform.

  • energy spectrum of superfluid turbulence with no normal fluid component
    Physical Review Letters, 2002
    Co-Authors: Tsunehiko Araki, Makoto Tsubota, Sergey K Nemirovskii
    Abstract:

    : The energy of superfluid turbulence without the normal fluid is studied numerically under the vortex filament model. Time evolution of the Taylor-Green vortex is calculated under the full nonlocal Biot-Savart Law. It is shown that for k<2pi/l the energy spectrum is very similar to the Kolmogorov's -5/3 Law which is the most important statistical property of the conventional turbulence, where k is the wave number of the Fourier component of the velocity field and l is the average intervortex spacing. The vortex length distribution converges to a scaling property reflecting the self-similarity of the tangle.

B.j. Fasenfest - One of the best experts on this subject based on the ideXlab platform.

  • Performance of Low-Rank QR Approximation of the Finite Element Biot–Savart Law
    IEEE Transactions on Magnetics, 2007
    Co-Authors: D.a. White, B.j. Fasenfest
    Abstract:

    In this paper, we present a low-rank QR method for evaluating the discrete Biot-Savart Law. Our goal is to develop an algorithm that is easily implemented on parallel computers. It is assumed that the known current density and the unknown magnetic field are both expressed in a finite-element expansion, and we wish to compute the degrees-of-freedom (DOF) in the basis function expansion of the magnetic field. The matrix that maps the current DOF to the field DOF is full, but if the spatial domain is properly partitioned the matrix can be written as a block matrix, with blocks representing distant interactions being low rank and having a compressed QR representation. While an octree partitioning of the matrix may be ideal, for ease of parallel implementation, we employ a partitioning based on number of processors. The rank of each block (i.e., the compression) is determined by the specific geometry and is computed dynamically. In this paper, we provide the algorithmic details and present computational results for large-scale computations

  • A QR Accelerated Volume-to-Surface Boundary Condition for the Finite-Element Solution of Eddy-Current Problems
    IEEE Transactions on Magnetics, 2007
    Co-Authors: D.a. White, B.j. Fasenfest, R. Rieben, Mark L. Stowell
    Abstract:

    We are concerned with the solution of time-dependent electromagnetic eddy-current problems using a finite-element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. To meet this requirement, we propose a volume-to-surface boundary condition based on the Biot-Savart Law. We found the Biot-Savart approach to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart Law

  • A QR accelerated volume-to-surface boundary condition for finite element solution of eddy current problems
    2006
    Co-Authors: D.a. White, B.j. Fasenfest, R. Rieben, M Stowell
    Abstract:

    We are concerned with the solution of time-dependent electromagnetic eddy current problems using a finite element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. We propose a Biot-Savart Law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart Law.

  • Performance of Low-Rank QR Approximation of the Finite Element Biot-Savart Law
    IEEE Transactions on Magnetics, 2006
    Co-Authors: D.a. White, B.j. Fasenfest
    Abstract:

    In this paper, we present a low-rank QR method for evaluating the discrete Biot-Savart Law. Our goal is to develop an algorithm that is easily implemented on parallel computers. It is assumed that the known current density and the unknown magnetic field are both expressed in a finite-element expansion, and we wish to compute the degrees-of-freedom (DOF) in the basis function expansion of the magnetic field. The matrix that maps the current DOF to the field DOF is full, but if the spatial domain is properly partitioned the matrix can be written as a block matrix, with blocks representing distant interactions being low rank and having a compressed QR representation. While an octree partitioning of the matrix may be ideal, for ease of parallel implementation, we employ a partitioning based on number of processors. The rank of each block (i.e., the compression) is determined by the specific geometry and is computed dynamically. In this paper, we provide the algorithmic details and present computational results for large-scale computations

  • Performance of Low-Rank QR Approximation of the Finite Element Biot-Savart Law
    2006 12th Biennial IEEE Conference on Electromagnetic Field Computation, 2006
    Co-Authors: D.a. White, B.j. Fasenfest
    Abstract:

    We are concerned with the computation of magnetic fields from known electric currents in the finite element setting. In finite element eddy current simulations it is necessary to prescribe the magnetic field (or potential, depending upon the formulation) on the conductor boundary. In situations where the magnetic field is due to a distributed current density, the Biot-Savart Law can be used, eliminating the need to mesh the non-conducting regions. Computation of the Biot-Savart Law can be significantly accelerated using a low-rank QR approximation. We review the low-rank QR method and report performance on selected problems

D.a. White - One of the best experts on this subject based on the ideXlab platform.

  • Performance of Low-Rank QR Approximation of the Finite Element Biot–Savart Law
    IEEE Transactions on Magnetics, 2007
    Co-Authors: D.a. White, B.j. Fasenfest
    Abstract:

    In this paper, we present a low-rank QR method for evaluating the discrete Biot-Savart Law. Our goal is to develop an algorithm that is easily implemented on parallel computers. It is assumed that the known current density and the unknown magnetic field are both expressed in a finite-element expansion, and we wish to compute the degrees-of-freedom (DOF) in the basis function expansion of the magnetic field. The matrix that maps the current DOF to the field DOF is full, but if the spatial domain is properly partitioned the matrix can be written as a block matrix, with blocks representing distant interactions being low rank and having a compressed QR representation. While an octree partitioning of the matrix may be ideal, for ease of parallel implementation, we employ a partitioning based on number of processors. The rank of each block (i.e., the compression) is determined by the specific geometry and is computed dynamically. In this paper, we provide the algorithmic details and present computational results for large-scale computations

  • A QR Accelerated Volume-to-Surface Boundary Condition for the Finite-Element Solution of Eddy-Current Problems
    IEEE Transactions on Magnetics, 2007
    Co-Authors: D.a. White, B.j. Fasenfest, R. Rieben, Mark L. Stowell
    Abstract:

    We are concerned with the solution of time-dependent electromagnetic eddy-current problems using a finite-element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. To meet this requirement, we propose a volume-to-surface boundary condition based on the Biot-Savart Law. We found the Biot-Savart approach to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart Law

  • A QR accelerated volume-to-surface boundary condition for finite element solution of eddy current problems
    2006
    Co-Authors: D.a. White, B.j. Fasenfest, R. Rieben, M Stowell
    Abstract:

    We are concerned with the solution of time-dependent electromagnetic eddy current problems using a finite element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. We propose a Biot-Savart Law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart Law.

  • Performance of Low-Rank QR Approximation of the Finite Element Biot-Savart Law
    IEEE Transactions on Magnetics, 2006
    Co-Authors: D.a. White, B.j. Fasenfest
    Abstract:

    In this paper, we present a low-rank QR method for evaluating the discrete Biot-Savart Law. Our goal is to develop an algorithm that is easily implemented on parallel computers. It is assumed that the known current density and the unknown magnetic field are both expressed in a finite-element expansion, and we wish to compute the degrees-of-freedom (DOF) in the basis function expansion of the magnetic field. The matrix that maps the current DOF to the field DOF is full, but if the spatial domain is properly partitioned the matrix can be written as a block matrix, with blocks representing distant interactions being low rank and having a compressed QR representation. While an octree partitioning of the matrix may be ideal, for ease of parallel implementation, we employ a partitioning based on number of processors. The rank of each block (i.e., the compression) is determined by the specific geometry and is computed dynamically. In this paper, we provide the algorithmic details and present computational results for large-scale computations

  • Performance of Low-Rank QR Approximation of the Finite Element Biot-Savart Law
    2006 12th Biennial IEEE Conference on Electromagnetic Field Computation, 2006
    Co-Authors: D.a. White, B.j. Fasenfest
    Abstract:

    We are concerned with the computation of magnetic fields from known electric currents in the finite element setting. In finite element eddy current simulations it is necessary to prescribe the magnetic field (or potential, depending upon the formulation) on the conductor boundary. In situations where the magnetic field is due to a distributed current density, the Biot-Savart Law can be used, eliminating the need to mesh the non-conducting regions. Computation of the Biot-Savart Law can be significantly accelerated using a low-rank QR approximation. We review the low-rank QR method and report performance on selected problems

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