A moving embedded boundary approach for the compressible Navier-Stokes equations in a block-structured adaptive refinement framework

•An unsplit, adaptive mesh, moving embedded boundary approach for the compressible Navier-Stokes equations is developed.•A least-squares estimation is used at the embedded boundary to accurately estimate pressure and skin-friction coefficients.•Viscous and inviscid flow scenarios are used for quantitative comparisons with analytical and experimental results.•Conservation errors are shown to diminish with refinement as demonstrated for a complex geometry test case.•Adaptive mesh refinement is shown to lead to well-behaved, converged solutions.