# Technologies

Navier-Stokes equation are partial differential equations, which are used to describe the motion of fluids. For most practical problems, Navier-Stokes equation does not afford an analytical solution thus necessitating the use of numerical methods. These methods compute physical quantities of interest, e.g. pressure, temperature, density and velocity as functions of time and space. An alternate approach to computational fluid dynamics is based on computing the time-evolution of the probability distribution of molecular velocities as modelled by the Boltzmann equation. All physical quantities of interest are then moments of this distribution function. This is called the** **Lattice-Boltzmann Method (LBM).

Sankhyasutra Labs utilizes numerical algorithms based on LBM to compute macroscopic quantities of interest, such as pressure, temperature, density and velocity. We use a highly efficient and accurate numerical algorithm for LBM to solve multi-physics models involving various physics phenomena viz, fluid flow, heat transfer, chemical reactions and phase transition. For rarefied gas flows, we use Direct Simulation Monte Carlo** **(DSMC) method, to solve the Boltzmann equation.

Innovations included in our solvers span across the software stack from mathematical models to efficient data structures and highly optimized parallel software implementation. Our simulation technology does not use any empirical turbulence models and uses optimisations based on first principles of physics. These innovations ensure that the results obtained are reliable and accurate without requiring unreasonable computational time. We also have an optimally architected custom-built High Performance Computing** **(HPC) cluster, which is among most powerful HPC systems in India. Applications of our technologies span various industries including but not limited to Automotive, Aerospace, Chemical & Petrochemical, Semiconductor industries.