Research on the Solution and Simulation of the Two-Dimensional Heat Equation

Abstract

Numerical calculation methods with high precision and fast speed are crucial for solving heat conduction problems, a method for solving and simulating the two-dimensional heat conduction process was proposed. This method discretized the two-dimensional heat equation in time and space; then combined the modified Crank-Nicolson method with the alternating direction implicit method to obtain the discrete equations of each node; then the algebraic equations was solved and combined with the Richardson extrapolation method to improve the convergence speed of the calculation; Finally, the two-dimensional heat conduction process was simulated by computer graphics technology, and the dynamic visualization of the temperature field in the two-dimensional heat conduction region was realized. The method is second-order convergent both in time and space, and its order is increased from the second order to the fourth order when combined with the Richardson extrapolation method. Experiments showed that this method can stably realize the simulation and dynamic visualization the of two-dimensional heat conduction process.