TY - JOUR
T1 - A Discrete Flux Scheme for Aerodynamic and Hydrodynamic Flows
AU - S. C. Fu, R. M. C. So & W. W. F. Leung
JO - Communications in Computational Physics
VL - 5
SP - 1257
EP - 1283
PY - 2011
DA - 2011/05
SN - 9
DO - http://doi.org/10.4208/cicp.311009.241110s
UR - https://global-sci.org/intro/article_detail/cicp/7550.html
KW - 
AB - <p style="text-align: justify;">The objective of this paper is to seek an alternative to the numerical simulation
of the Navier-Stokes equations by a method similar to solving the BGK-type
modeled lattice Boltzmann equation. The proposed method is valid for both gas and
liquid flows. A discrete flux scheme (DFS) is used to derive the governing equations
for two distribution functions; one for mass and another for thermal energy. These
equations are derived by considering an infinitesimally small control volume with a
velocity lattice representation for the distribution functions. The zero-order moment
equation of the mass distribution function is used to recover the continuity equation,
while the first-order moment equation recovers the linear momentum equation. The
recovered equations are correct to the first order of the Knudsen number (Kn); thus,
satisfying the continuum assumption. Similarly, the zero-order moment equation of
the thermal energy distribution function is used to recover the thermal energy equation.
For aerodynamic flows, it is shown that the finite difference solution of the DFS
is equivalent to solving the lattice Boltzmann equation (LBE) with a BGK-type model
and a specified equation of state. Thus formulated, the DFS can be used to simulate a
variety of aerodynamic and hydrodynamic flows. Examples of classical aeroacoustics,
compressible flow with shocks, incompressible isothermal and non-isothermal Couette
flows, stratified flow in a cavity, and double diffusive flow inside a rectangle are used
to demonstrate the validity and extent of the DFS. Very good to excellent agreement
with known analytical and/or numerical solutions is obtained; thus lending evidence
to the DFS approach as an alternative to solving the Navier-Stokes equations for fluid
flow simulations.</p>