A New Lattice Boltzmann Method.
Lie, Han Cheng.
- The Lattice Boltzmann Equation (LBE) is used in computational fluid dynamics (CFD) to simulate fluid flow. It is a difference equation that specifies the state of the fluid after a time step of fixed length, and may be considered a discrete-time equation since the time step is fixed. The discrete-time LBE (DTLBE) has a flaw in that the state of the fluid is not known during the fixed-length time ... read morestep. In this paper, we present the DTLBE, derive a continuous-time LBE (CTLBE) from the DTLBE, and present a theoretical and numerical analysis of the CTLBE. Although the CTLBE is computationally more intensive than the DTLBE - it takes more floating-point operations to evolve the fluid using the CTLBE than when using the DTLBE - we find that the CTLBE is more accurate with respect to the Incompressible-Navier Stokes Equations in simulating fluid flow. Furthermore, the CTLBE allows for variable and adaptive time stepping, thus enhancing the flexibility of Lattice Boltzmann Methods for simulating fluid flow.read less