Study on a New Numerical Method for Solving Heat Conduction Problems

In this paper, a new numerical method, the half boundary method (HBM) is studied. HBM reduced the order of the basic equation by substitution, and then calculated the relationship between the adjacent two nodes on the geometric model by integral solution, and recurred to the relationship between any node on the model and the boundary point. HBM is a small-storage, high-precision, fast and efficient numerical calculation method, with few unknowns and non-iterative innovation nodes, which can meet the requirements of accurate acquisition of real-time temperature field in the case of less computational resources. HBM calculation schemes of one and two dimensions in Cartesian coordinate system are derived in detail. The result of HBM calculation is compared with the result of FVM calculation in the corresponding example. It is found that when the number of nodes is small, the calculation accuracy of HBM is much higher than that of FVM. When the number of nodes is large, both HBM and FVM have high accuracy, but HBM calculation time is shorter. HBM calculation results is provided by MATLAB programs.