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<p class="noindent">We present an unsplit method for the time-dependent compressible Navier–Stokes equations in two and three dimensions. We use a conservative, second-order Godunov algorithm. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We solve for viscous and conductive terms with a second-order semiimplicit algorithm. We demonstrate second-order accuracy in solutions of smooth problems in smooth geometries and demonstrate robust behavior for strongly discontinuous initial conditions in complex geometries. </p>

A cartesian grid embedded boundary method for the compressible Navier–Stokes equations