Abstract: A method is presented here for constructing two-dimensional Delaunay triangulation with a new automatic point creation technique.This technique is based on the idea of advancing-front method to achieve good geometry flexibility.The main steps are as follows:The initial triangulation is generated first,according to the given border set.In the initial triangulation usually there are lots of triangles with very small minimum angles which will seriously decrease computational accuracy.The new nodes are introduced with advancing-front method,and added into the existing mesh according to Bowyer-Watson algorithm simultaneously.The procedure is repeated until no more improvement of the grid can be achieved by inserting the new nodes.Its application to triangulating combustor fluid shows that the resulted grids have great regularity and boundary quality.