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A new parallel, fully implicit, anisotropic blockbased adaptive mesh refinement (AMR) finite-volume scheme is proposed, described and demonstrated for the prediction of laminar, compressible, viscous flows associated with unsteady oblique shock reflection processes. The proposed finite-volume method provides numerical solutions to the Navier-Stokes equations governing the flow of polytropic gases in an accurate and efficient manner on twodimensional, body-fitted, multi-block meshes consisting of quadrilateral computational cells. The combination of the anisotropic AMR and parallel implicit time-marching techniques adopted is shown to readily facilitate the simulation of challenging and complex shock interaction problems, as represented by the time-accurate predictions of unsteady oblique shock reflection configurations with fully resolved internal shock structures.Keywords Oblique shock reflections · Parallel implicit finite-volume methods · Anisotropic adaptive mesh refinement (AMR) · Newton-Krylov-Schwarz (NKS)

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