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Full-Text Articles in Astrophysics and Astronomy
Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, S. Williams, J. B. Bell
Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, S. Williams, J. B. Bell
Faculty Publications
This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau–Lifshitz Navier–Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently developed solver for the LLNS equations based on third-order Runge–Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the …
Numerical Methods For The Stochastic Landau-Lifshitz Navier-Stokes Equations, Alejandro Garcia, J. B. Bell, S. Williams
Numerical Methods For The Stochastic Landau-Lifshitz Navier-Stokes Equations, Alejandro Garcia, J. B. Bell, S. Williams
Faculty Publications
The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack’s two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk …
Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, Sarah Williams, John B. Bell
Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, Sarah Williams, John B. Bell
Alejandro Garcia
This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau–Lifshitz Navier–Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently developed solver for the LLNS equations based on third-order Runge–Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the …
Numerical Methods For The Stochastic Landau-Lifshitz Navier-Stokes Equations, Alejandro Garcia, John B. Bell, Sarah Williams
Numerical Methods For The Stochastic Landau-Lifshitz Navier-Stokes Equations, Alejandro Garcia, John B. Bell, Sarah Williams
Alejandro Garcia
The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack’s two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk …