Calculation Experiment Technology

There are two common approaches for numerical solution of continuum equations in mechanics: Lagrangian and Eulerian. The choice usually depends on exploiting specific features of these approaches that are suitable for the problem at hand. In the Lagrangian approach the computational grid that discretizes the domain deforms with the material. However Lagrangian method is not suitable for applications involving large distortion and large rotation, or for cases where boundary itself is modified as the solution proceeds. On the other hand, in the Eulerian approach the computational grid is fixed in space. The material moves through this grid as it flows and deforms. Even though large distortions are handled easily in this method, interface tracking and contact surface algorithms pose considerable difficulty. Novel methods have been developed that discretize the continuum domain by discrete Lagrangian particles. Harlow’s Particle In Cell (PIC) method [1] may be considered to be one of the precursors. This method eliminates the shortcomings of the traditional Lagrangian and Eulerian methods while retaining the good aspects of them. This method allows one to solve a broader class of problems by allowing large distortions and efficient calculation at interfaces. The PIC method also allows precise distinction of material boundaries. In spite of these advantages the PIC method shows certain limitations for problems where variables are history dependent, for example in elasto-plasticity, viscoelasticity, various relaxation processes, and for problems dealing with low pressures. Another shortcoming of this approach is that the solution fluctuates due to the method of discretization of mass, energy and momentum, and the way by which density is calculated. A more serious limitation arises out of the complexity of pressure calculation in a mixed cell. From the above mentioned of existing computational methods for non-stationary continua it is clear that none of them satisfy the requirements for large-scale computation. The grid and particle methods such as PIC and GAP [2] seem to possess the best characteristics in this regard. Hence these methods were taken up as a basis for developing a new method – the method of individual particles (1979, developed under the scientific leaderships of Prof. V.F.Minin) to extend the areas of applicability of the particle methods. Some particle methods in Astrophysical Fluid Dynamics are discussed and available at [3].