A transfinite interpolation method of grid generation based on multipoints

In this work two algebraic grid generation methods based on the Soni-linear and Soni-Hermite transfinite interpolation methods, respectively, are developed. The necessary data of the transfinite interpolation formulas, such as coordinates and grid angles, are determined by more than one points along all the boundaries. The number of dependent points increases and the influence factors associated to these points decrease as the point of interesting moves away from a boundary. Several test cases are examined to show the proposed methods' capability.