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The Ziman formulation of electrical conductivity is tested in warm and hot dense matter using the pseudo-atom molecular dynamics method. Several implementation options that have been widely used in the literature are systematically tested through a comparison to accurate but expensive Kohn-Sham density functional theory molecular dynamics (KS-DFT-MD) calculations. The comparison is made for several elements and mixtures and for a wide range of temperatures and densities, and reveals a preferred method that generally gives very good agreement with the KS-DFT-MD results, but at a fraction of the computational cost.PACS numbers: 52.25.Fi, 52.27.Gr * Electronic address: starrett@lanl.gov 1 Hereafter referred to as quantum molecular dynamics (QMD).

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High-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme’s order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.