A Compatible, Energy and Symmetry Preserving Lagrangian Hydrodynamics Algorithm in Three-Dimensional Cartesian Geometry

2000 ◽  
Vol 157 (1) ◽  
pp. 89-119 ◽  
Author(s):  
E.J. Caramana ◽  
C.L. Rousculp ◽  
D.E. Burton
Keyword(s):  
Three Dimensional ◽  
Cartesian Geometry ◽  
Lagrangian Hydrodynamics

Two new three-dimensional contact algorithms for staggered Lagrangian Hydrodynamics

2014 ◽  
Vol 267 ◽  
pp. 247-285
Author(s):  
Zupeng Jia ◽  
Xiangfei Gong ◽  
Shudao Zhang ◽  
Jun Liu
Keyword(s):  
Three Dimensional ◽  
Lagrangian Hydrodynamics

Implementation of 2D Domain Decomposition in the UCAN Gyrokinetic Particle-in-Cell Code and Resulting Performance of UCAN2

2016 ◽  
Vol 19 (1) ◽  
pp. 205-225 ◽  
Author(s):  
Jean-Noel G. Leboeuf ◽  
Viktor K. Decyk ◽  
David E. Newman ◽  
Raul Sanchez
Keyword(s):  
Domain Decomposition ◽  
Parallel Implementation ◽  
Three Dimensional ◽  
Massively Parallel ◽  
Problem Size ◽  
Time Step ◽  
Particle In Cell ◽  
Minor Radius ◽  
Efficient Charge ◽  
Cartesian Geometry

AbstractThe massively parallel, nonlinear, three-dimensional (3D), toroidal, electrostatic, gyrokinetic, particle-in-cell (PIC), Cartesian geometry UCAN code, with particle ions and adiabatic electrons, has been successfully exercised to identify non-diffusive transport characteristics in present day tokamak discharges. The limitation in applying UCAN to larger scale discharges is the 1D domain decomposition in the toroidal (or z-) direction for massively parallel implementation using MPI which has restricted the calculations to a few hundred ion Larmor radii or gyroradii per plasma minor radius. To exceed these sizes, we have implemented 2D domain decomposition in UCAN with the addition of the y-direction to the processor mix. This has been facilitated by use of relevant components in the P2LIB library of field and particle management routines developed for UCLA's UPIC Framework of conventional PIC codes. The gyro-averaging specific to gyrokinetic codes is simplified by the use of replicated arrays for efficient charge accumulation and force deposition. The 2D domain-decomposed UCAN2 code reproduces the original 1D domain nonlinear results within round-off. Benchmarks of UCAN2 on the Cray XC30 Edison at NERSC demonstrate ideal scaling when problem size is increased along with processor number up to the largest power of 2 available, namely 131,072 processors. These particle weak scaling benchmarks also indicate that the 1 nanosecond per particle per time step and 1 TFlops barriers are easily broken by UCAN2 with 1 billion particles or more and 2000 or more processors.

The Fast Three-Dimensional Space-Time Neutron Kinetic Model for Cartesian Geometry and Cylindrical Geometry

2016 ◽  
Author(s):  
Zhifeng Li ◽  
Hongchun Wu ◽  
Chenghui Wan ◽  
Tianliang Hu
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Cylindrical Geometry ◽  
Neutron Diffusion ◽  
Diffusion Kinetics ◽  
Dimensional Space Time ◽  
Cartesian Geometry ◽  
Predictor Corrector ◽  
Three Dimensional Space

In order to raise computation speed on the premise of enough numerical accuracy, the Predictor-Corrector Improved Quasi-Static (PC-IQS) method and Nodal Green’s Function Method (NGFM) were combined to solve the three-dimensional space-time neutron diffusion kinetics problems for Cartesian geometry. In addition, the improved quasi-static method and the Krylov algorithm were applied to solve the three-dimensional space-time neutron diffusion kinetics problems for cylindrical geometry. Based on the proposed model, the program of three-dimensional neutron space-time kinetic code has been tested by the two-dimensional and three-dimensional transient numerical benchmarks. The numerical results obtained by this work were in good agreement with the reference solutions.

The Error Bounds for Three-Dimensional Nodal LTSN Method

2008 ◽  
Author(s):  
Eliete Biasotto Hauser ◽  
Ruben Panta Pazos ◽  
Marco T. M. B. Vilhena ◽  
Ricardo C. Barros
Keyword(s):  
Spectral Analysis ◽  
Analytical Solution ◽  
Laplace Transform ◽  
Error Bounds ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Exponential Functions ◽  
Decay Constants ◽  
The Laplace Transform ◽  
Cartesian Geometry

In this paper we present a proof about the convergence of the 3D Nodal-LTSN Method in order to solve the transport problem in a parallelepiped domain. For that, we define functions associated to the errors, one in the approximated flux, another in the quadrature formula and establish a relation between them. We present a Nodal-LTSN method to generate an analytical solution for discrete ordinates problems in three-dimensional cartesian geometry. We first transverse integrate the SN equations and then we apply the Laplace transform. The essence of this method is the diagonalization of the LTSN transport matrices and the spectral analysis garantees this. The transverse leakage terms that appear in the transverse integrated SN equations are represented by exponential functions with decay constants that depend on the characteristics of the material of the medium the particles leave behind. We present numerical results generated by the offered method applied to typical shielding model problems.

scholarly journals Multilayered solar interface dynamos: from a Cartesian kinematic dynamo to a spherical dynamic dynamo

2007 ◽  
Vol 3 (S247) ◽  
pp. 22-32
Author(s):  
Kit H. Chan ◽  
Xinhao Liao ◽  
Keke Zhang
Keyword(s):  
Magnetic Field ◽  
Convection Zone ◽  
Three Dimensional ◽  
Dynamo Model ◽  
Dynamic Feedback ◽  
Spherical System ◽  
Dynamic Interface ◽  
Cartesian Geometry ◽  
Interface Matching ◽  
Dynamo Process

AbstractThe existence of the solar tachocline, a thin differentially rotating layer at the base of the convection zone which is inferred from helioseismology, leads to the concept of an interface dynamo. The tachocline is magnetically coupled to the radiative interior and the overlying convection zone. A multilayered interface dynamo is required to describe the dynamo process involved. We first discuss a two-dimensional multilayered interface dynamo model in cartesian geometry consisting of four horizontal layers with different magnetic diffusivities magnetically coupled by the three sets of interface matching conditions for the generated magnetic field. Exact solutions of the coupled dynamo system are obtained in this model. We then discuss a fully three-dimensional and multi-layered spherical dynamic interface dynamo using a finite element method based on the three-dimensional tetrahedralization of the whole spherical system. The spherical dynamic interface dynamo also consists of four magnetically coupled zones. In the convection zone, the fully three-dimensional dynamic feedback of Lorentz forces is taken into account. It is shown that the dynamo is characterized by a strong toroidal magnetic field, selects dipolar symmetry and propagates equatorward.

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