TY - GEN
T1 - Semi-analytical solution of the density profile for a gas close to a solid wall
AU - Akker, van den, E.A.T.
AU - Frijns, A.J.H.
AU - Nedea, S.V.
AU - Steenhoven, van, A.A.
PY - 2009
Y1 - 2009
N2 - To reduce the CPU time needed for Molecular Dynamics (MD) simulations or Direct Simulation Monte Carlo (DSMC), an effort is made to reduce the equilibration period. A semi-analytical model for the equilibrium situation of particle simulations is developed, such that the initial positions and velocities in a particle model such as MD or DSMC can be chosen close to the equilibrium situation.
A time-averaged intermolecular force and a time-averaged pressure are derived from the density distribution. It is shown that the intermolecular force is short-ranged and a result of density variations. For uniform densities, the time-averaged pressure is shown to correspond to the empirically determined equation of state for hard sphere particles. For non-uniform densities, the approximation is no longer valid and a new linear approximation is derived. It is shown that this linear approximation is valid even for dense gases.
With this information, a semi-analytical model for the equilibrium density is derived and solved numerically in detail for the problem of particles close to a hard wall. In this situation density oscillations occur. The numerical results also show these density oscillations, indistinguishable from MD. The CPU time needed to generate the density profile of particles close to a wall was less than one second, whereas the CPU time needed to perform the Molecular Dynamics simulations to reach the same equilibrium with the same accuracy was several hours. Therefore this method can be used to reduce computation time of simulations.
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AB - To reduce the CPU time needed for Molecular Dynamics (MD) simulations or Direct Simulation Monte Carlo (DSMC), an effort is made to reduce the equilibration period. A semi-analytical model for the equilibrium situation of particle simulations is developed, such that the initial positions and velocities in a particle model such as MD or DSMC can be chosen close to the equilibrium situation.
A time-averaged intermolecular force and a time-averaged pressure are derived from the density distribution. It is shown that the intermolecular force is short-ranged and a result of density variations. For uniform densities, the time-averaged pressure is shown to correspond to the empirically determined equation of state for hard sphere particles. For non-uniform densities, the approximation is no longer valid and a new linear approximation is derived. It is shown that this linear approximation is valid even for dense gases.
With this information, a semi-analytical model for the equilibrium density is derived and solved numerically in detail for the problem of particles close to a hard wall. In this situation density oscillations occur. The numerical results also show these density oscillations, indistinguishable from MD. The CPU time needed to generate the density profile of particles close to a wall was less than one second, whereas the CPU time needed to perform the Molecular Dynamics simulations to reach the same equilibrium with the same accuracy was several hours. Therefore this method can be used to reduce computation time of simulations.
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U2 - 10.1007/978-90-481-2626-2_3
DO - 10.1007/978-90-481-2626-2_3
M3 - Conference contribution
SN - 978-90-481-2625-5
T3 - IUTAM Bookseries
SP - 35
EP - 50
BT - IUTAM Symposium on Advances in Micro- and Nanofluidics, Dresden, Germany, September 6-8, 2007
A2 - Ellero, M.
A2 - Hu, X.
A2 - Fröhlich, J.
A2 - Adams, N.
PB - Springer
CY - Berlin
T2 - IUTAM Symposium on Advances in Micro- and Nanofluidics, September 6-8, 2007, Dresden, Germany
Y2 - 6 September 2007 through 8 September 2007
ER -