Derivation and Numerical Simulation of Regularized (Observable) Euler Equations

Abstract

ows. A regularization technique for the Burgers equation (Norgard and Mohseni 2008) was recently reported. This inviscid regulariza- tion was extended to one-dimensional compressible Euler equations in 2009 (Norgard and Mohseni 2009). This investigation presents a formal derivation of these equations from basic principles. Our previous results are extended to multidimensional compressible and incompressible Euler equations. We dene a new observable divergence based on uxes calculated from observable quantities at a desired scale. An observable divergence theorem is then proved and applied in the derivation of the regularized equations. It is shown that the derived equations reduces to inviscid Leray ow model in the limit of incompressibil- ity. It is expected that this technique simultaneously regularizes shocks and turbulence for compressible and incompressible ows. Finally, numerical simulations are presented for the compressible one-dimensional observable Euler equations.