Application of a modified finite element method to the time-dependent thermal convection of a liquid metal
Starting with the Galerkin finite-element method and the simplest appropriate isoparametric element for modeling the Navier-Stokes equations, the spatial approximation is modified in two ways in the interest of cost-effectiveness: the mass matrix is lumped and all coefficient matrices are generated via one-point quadrature. After appending a correction term to the diffusion matrices, the modified semi-discretized equations are integrated in time using the explicit Euler method in a special way to compensate for that portion of the time truncation error which is intolerable for advection-dominated flows. The scheme is completed by the introduction of a subcycling strategy which permits less frequent updates of the pressure field with little loss of accuracy. After summarizing these techniques, a simulation of free convection in a two-dimensional box at Ra = 10/sup 5/ and Pr = 0.01 is described.
- Research Organization:
- Lawrence Livermore National Lab., CA (USA)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5890884
- Report Number(s):
- UCRL-88990; CONF-830803-8; ON: DE83009847
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONVECTION
DIFFERENTIAL EQUATIONS
ELEMENTS
EQUATIONS
FINITE ELEMENT METHOD
FLUIDS
LIQUID METALS
LIQUIDS
MATRICES
METALS
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
TWO-DIMENSIONAL CALCULATIONS