1979 Volume 65 Issue 12 Pages 1737-1746
A proposal has been made for the classification of numerical methods to two groups; one is based on a differential equation and the other is not. The latter “Direct Method”, which means that a finite-difference equation is derived directly from the phenomenon, may be divided into Outer and Inner Nodal Point Methods (ONP Method and INP Method). The typical ONP Method is the matrix method developed by the authors, where the nodal point is designated on the element boundary. In the INP Method the nodal point is designated within the element and the nodal domain is the element itself. On the basis of this classification and some discussion on the conventional methods, an improved INP Method has been developed and the outline with finite-difference equations for energy balance, mass balance and momentum equations for potential flow is presented. In addition, numerical examples for solidification problems are demonstrated and discussed. Although the combination of right triangle elements forming a rectangle can not be used in the proposed method, it has the same advantage as the ONP Method over the conventional finite element method and is superior to the ONP Method in simplicity and computing time.