Abstract: Difference numerical simulation for two dimensional thermal conduction equation is studied.Using the variational principle,the difference scheme with thermal-flux form in the irregular structured mesh is presented.The thermal flux as an unknown function is obtained by minimizing the functional and solved with the equation of temperature function simultaneously.This scheme overcomes the defects of general nine-point schemes,which have to calculate the thermal conduction coefficients on the cell boundaries and the temperatures located in the cell vertices by interpolation.

Key words: variational principle, two dimensional thermal conduction equation, irregular structured mesh