Improvement of the flow formulation by recovery of the hydrostatic pressure using the finite point method

Abstract

Most of the existing numerical methods based on penalty technique, lead to pressure fields, which are not satisfactory especially when crude meshes are used. The present work for the first time, using a simple and effective finite point approach approximates the total hydrostatic stresses. By this new technique, the nodal hydrostatic pressure values are calculated so that the gradient of hydrostatic pressure satisfies the equilibrium equation, with regard to the current distribution of deviatoric stresses. This approach is verified using a cantilever beam with known analytical stress field. It is also applied to a typical 2D axisymmetric bulk metal forming process. The calculated pressure field is then compared with available solutions. The results of the present approach are very encouraging.