15,266 research outputs found
A collocated finite volume scheme to solve free convection for general non-conforming grids
We present a new collocated numerical scheme for the approximation of the
Navier-Stokes and energy equations under the Boussinesq assumption for general
grids, using the velocity-pressure unknowns. This scheme is based on a recent
scheme for the diffusion terms. Stability properties are drawn from particular
choices for the pressure gradient and the non-linear terms. Numerical results
show the accuracy of the scheme on irregular grids
Solving the Boltzmann equation deterministically by the fast spectral method : application to gas microflows
Based on the fast spectral approximation to the Boltzmann collision operator, we present an accurate and efficient deterministic numerical method for solving the Boltzmann equation. First, the linearised Boltzmann equation is solved for Poiseuille and thermal creep flows, where the influence of different molecular models on the mass and heat flow rates is assessed, and the Onsager-Casimir relation at the microscopic level for large Knudsen numbers is demonstrated. Recent experimental measurements of mass flow rates along a rectangular tube with large aspect ratio are compared with numerical results for the linearised Boltzmann equation. Then, a number of two-dimensional micro flows in the transition and free molecular flow regimes are simulated using the nonlinear Boltzmann equation. The influence of the molecular model is discussed, as well as the applicability of the linearised Boltzmann equation. For thermally driven flows in the free molecular regime, it is found that the magnitudes of the flow velocity are inversely proportional to the Knudsen number. The streamline patterns of thermal creep flow inside a closed rectangular channel are analysed in detail: when the Knudsen number is smaller than a critical value, the flow pattern can be predicted based on a linear superposition of the velocity profiles of linearised Poiseuille and thermal creep flows between parallel plates. For large Knudsen numbers, the flow pattern can be determined using the linearised Poiseuille and thermal creep velocity profiles at the critical Knudsen number. The critical Knudsen number is found to be related to the aspect ratio of the rectangular channel
A Fast Poisson Solver of Second-Order Accuracy for Isolated Systems in Three-Dimensional Cartesian and Cylindrical Coordinates
We present an accurate and efficient method to calculate the gravitational
potential of an isolated system in three-dimensional Cartesian and cylindrical
coordinates subject to vacuum (open) boundary conditions. Our method consists
of two parts: an interior solver and a boundary solver. The interior solver
adopts an eigenfunction expansion method together with a tridiagonal matrix
solver to solve the Poisson equation subject to the zero boundary condition.
The boundary solver employs James's method to calculate the boundary potential
due to the screening charges required to keep the zero boundary condition for
the interior solver. A full computation of gravitational potential requires
running the interior solver twice and the boundary solver once. We develop a
method to compute the discrete Green's function in cylindrical coordinates,
which is an integral part of the James algorithm to maintain second-order
accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics
code, and perform various tests to check that our solver is second-order
accurate and exhibits good parallel performance.Comment: 24 pages, 13 figures; accepted for publication in ApJ
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