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We present a new method for coupling molecular dynamics (MD) and continuum mechanics simulations that is based on the projection of the MD solution onto the coarse scale shape functions. This projection, or “bridging scale”, represents that part of the solution that is obtainable by both solution methods. By subtracting the bridging scale from the total solution, we arrive at a coarse-fine decomposition that, by a proper choice of projection operator, decouples the kinetic energy of the two simulations. The resulting decomposition can be used in a finite-temperature simulation method in which MD is used only in a localized region, while the continuum simulation covers the entire domain, including the MD region to which it is coupled. One major advantage of this approach is that separate time step sizes can be used in the two simulations, so that the coarse scale time step is not limited to the time scale of the atomic vibrations present in the fine scale. Example problems are demonstrated on a 1D lattice, for which the method is shown to be accurate both for harmonic and anharmonic interatomic potentials. [Copyright &y& Elsevier]

A parallel computational implementation of a meshfree method—the reproducing kernel particle method (RKPM)—is used for 3-D implicit CFD analysis. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. Using this enrichment along the essential boundaries produces results that more closely match experimental and analytical results for a flow past a cylinder problem than does either the finite-element method or other meshfree methods that require matrix inversion for the application of essential boundary conditions. This technique also allows the efficient parallelization of the algorithm and leads to higher parallel speedups than do other boundary condition implementations, many of which involve inherently serial steps; this is important, because the expense of meshfree computations makes parallelization crucial for large-size problems. The performance of the parallelization technique and the accuracy of the implicit CFD algorithm are demonstrated in two example problems. [Copyright &y& Elsevier]

Abstract The level set method for modeling multi-fluid interfaces gives a simple approach for the simulation of multiphase flow problems. However, many of the components of this method, such as the redistancing of the level set function and discretization of the singular surface tension force, become more difficult on unstructured meshes in a control volume framework; furthermore, these operations are shown to lead to errors in conservation of mass of the individual phases, as well as unphysical currents near the interface. This paper presents a novel formulation for the level set method combined with a balanced-force algorithm using a control volume finite element method (CVFEM) for unstructured grids. A diffuse interface description is used, allowing a straightforward inclusion of surface tension forces; we show that by consistently evaluating the pressure gradient and surface tension, we are able to discretely balance these two forces and suppress any parasitic currents given a prescribed curvature. By converting the redistancing equation to a form that is suitable for CVFEM and enforcing a constraint directly linked with the phase fraction in each cell, we are able conserve mass and preserve the shape of the interface to a high degree of accuracy in multiphase flow problems with high density and viscosity ratios. The accuracy of the of our proposed method is assessed by comparing with benchmark results from the literature. Highlights • A novel level set formulation utilizing CVFEM is proposed. • A balanced-force algorithm is formulated for purely unstructured meshes. • The redistancing equation is reformulated to allow higher order upwinding methods. • A new constraint is introduced to preserve the shape of the interface. • Benchmark examples show convergence for high density and viscosity ratio problems. [ABSTRACT FROM AUTHOR]