Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations
Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- DE-ACO2-09CH11466
- OSTI ID:
- 969310
- Report Number(s):
- PPPL-4476; TRN: US1000272
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
BOUNDARY CONDITIONS
EFFICIENCY
FLEXIBILITY
MAGNETOHYDRODYNAMICS
PLASMA SIMULATION
PRESERVATION
REFINING
RELAXATION
SIMULATION
THERMAL CONDUCTION
THERMAL CONDUCTIVITY
TRANSPORT
VECTORS
Numerical Simulation
Numeriial Methods
Nonlinear Effects
Mathematical Physics
Supercomputers