Application of Vector Calculus to Numerical Simulation of Continuum Mechanics Problems

It is well known that vector–tensor notation is a compact and natural language for the mathematical formulation of continuum mechanics problems. Here we describe the application of vector technique to numerical simulation starting with a mathematical formulation. We provide an efficient numerical scheme and furnish an implementation as a computer program. As a result (in comparison with traditional “component” form), the two last steps are significantly simplified, especially for multidimensional problems with various boundary conditions in irregular geo- metries where nonorthogonal meshes are applied. Therefore, more attention can be focused on the physical nature of problems. Apart from the cleaner syntax, vector notation conserves the structure of traditional numerical algorithms and solves multidimensional problems with minimum additional programming effort. Complex practical applications of this technique are described as well.