wilson-2d.fee

# 2d problem from
# Gary L. Wilson, Roger A. Rydin & Seppo Orivuori (1988) A Comparison of Two
# Efficient Nonlinear Heat Conduction Methodologies Using a Two-Dimensional Time-Dependent
# Benchmark Problem, Nuclear Technology, 82:1, 94-105, DOI: 10.13182/NT88-A34120
# http://dx.doi.org/10.13182/NT88-A34120

PROBLEM thermal 2d
READ_MESH wilson-2d.msh

k(x,y) = 1 + 0.5*T(x,y)
rhocp(x,y) = 1 + 0.5*T(x,y)

BC heat q=1                GROUP left  GROUP bottom
BC temp T=limit(1e5*t,0,1) GROUP right GROUP top
T_0(x,y) = 0

end_time = 17.25

T_q1_ref = 2.3872
T_q2_ref = 1.1972
T_q3_ref = 1.5903
T_q4_ref = 1.5903

SOLVE_PROBLEM

# PRINT t
# WRITE_MESH wilson-2d-result.msh T

IF done
 INTEGRATE T OVER quadrant1 RESULT int_q1
 INTEGRATE T OVER quadrant2 RESULT int_q2
 INTEGRATE T OVER quadrant3 RESULT int_q3
 INTEGRATE T OVER quadrant4 RESULT int_q4
 area = 1.5^2

 PRINT abs(int_q1/area-T_q1_ref)+abs(int_q2/area-T_q2_ref)+abs(int_q3/area-T_q3_ref)+abs(int_q4/area-T_q4_ref)
ENDIF