Driven Shock in Three Dimensions: Euler Equations Versus Molecular Dynamics, and Navier-Stokes Equations

Isotropic and continuous localised perturbations in a stationary gas, created by an external point source, cause a spherically symmetric shock wave with the energy E(t) increasing in time t as E(t)∽ t^δ, where δ≥0. The analytical solution of the Euler equation providing the spatio-temporal behavior of the shock wave, is a classic problem in gas dynamics. The exact solution shows that the asymptotic behavior of non-dimensionalised thermodynamic quantities obey power law behavior in rescaled distance near the shock center with the exponents independent of δ. However, using Event Driven Molecular Dynamics Simulations, we find that the exact solution does not match with EDMD results, anywhere, mainly in terms of the power law exponents near the shock center. We show that this mismatch is due to ignoring the contribution of heat conduction and viscosity terms, and the mismatch between theory and numerics can be resolved by taking into account the Navier-Stokes equation. We showed that the direct numerical solution of Navier-Stokes equation captures these observed power law exponents in the EDMD simulations indicating the significance of viscosity and heat conduction in shock problems.