This paper presents a new finite-volume discretization of a generalised LatticeBoltzmann equation (LBE) on unstructured grids. This equation is the continuumLBE, with the addition of a second order time derivative ter...This paper presents a new finite-volume discretization of a generalised LatticeBoltzmann equation (LBE) on unstructured grids. This equation is the continuumLBE, with the addition of a second order time derivative term (memory), and is derivedfrom a second-order differential form of the semi-discrete Boltzmann equationin its implicit form. The new scheme, named unstructured lattice Boltzmann equationwith memory (ULBEM), can be advanced in time with a larger time-step than the previousunstructured LB formulations, and a theoretical demonstration of the improvedstability is provided. Taylor vortex simulations show that the viscosity is the same aswith standard ULBE and demonstrates that the new scheme improves both stabilityand accuracy. Model validation is also demonstrated by simulating backward-facingstep flow at low and moderate Reynolds numbers, as well as by comparing the reattachmentlength of the recirculating eddy behind the step against experimental andnumerical data available in literature.展开更多
文摘This paper presents a new finite-volume discretization of a generalised LatticeBoltzmann equation (LBE) on unstructured grids. This equation is the continuumLBE, with the addition of a second order time derivative term (memory), and is derivedfrom a second-order differential form of the semi-discrete Boltzmann equationin its implicit form. The new scheme, named unstructured lattice Boltzmann equationwith memory (ULBEM), can be advanced in time with a larger time-step than the previousunstructured LB formulations, and a theoretical demonstration of the improvedstability is provided. Taylor vortex simulations show that the viscosity is the same aswith standard ULBE and demonstrates that the new scheme improves both stabilityand accuracy. Model validation is also demonstrated by simulating backward-facingstep flow at low and moderate Reynolds numbers, as well as by comparing the reattachmentlength of the recirculating eddy behind the step against experimental andnumerical data available in literature.
