P. A. Skordos, Initial and boundary conditions for the Lattice Boltzmann method, Phys. Rev. E 48 (1993), 4823-4842.  Home/Search   Document Not in Database   Summary   APS   Related Articles   Check

....whichisvery importantinpractical situations. Further, I demonstrate experimentally that the discretization error of the lattice Boltzmann method decreases quadratically with finer resolution both in space and in time. My results on the lattice Boltzmann method havebeen published in Skordos [48], and have helped to bring the lattice Boltzmann method from the physicists world to the engineer s world. Apart from the lattice Boltzmann method, I examine twodifferentkinds of explicit finite difference methods. In chapter 4, I compare the lattice Boltzmann method against an incompressible ....

....resolution. For simplicity, let us assume that the resolution on the rightsideistwice the resolution on the left side. Traditional interpolation can be used to join the twofinite difference grids of different resolution. Further on, as wemovetothe right, wechange from finite In my earlier paper [48], I suggested that the densityatawall should be calculated as the average of the populations that bring fluid into the boundary node from inner nodes and other neighboring boundary nodes. Further numerical experiments, however, indicate that the average of the populations after bouncek, ....

[Article contains additional citation context not shown here]

P.A. Skordos. Initial and boundary conditions for the lattice Boltzmann method. Physical Review E,48(6):" 42, December 1993.

.... Theta with ae(u Omega u Gamma 2 3 S[u] as suggested by (26) we obtain the distribution function F (ae; u; v) ae 1 3u k v k 9 2 u k u l Gamma 2 3 S kl [u] v k v l Gamma ffi kl =3) f (v) 11 where S[u] has to be calculated by taking derivatives of u. In [18], a distribution function similar to F has been used to set up suitable boundary and initial values for the lattice Boltzmann method. Since the higher moments q and s are negligible and Theta is given essentially through ae and u, F can be viewed as an approximate inverse of the moment map f 7 ....

.... is given essentially through ae and u, F can be viewed as an approximate inverse of the moment map f 7 (hfi ; hvfi =ffl) This observation can be used to translate initial and boundary conditions which are given in terms of ae and u into corresponding conditions for the occupation numbers (see [18] for details) In [19] a scheme has been introduced which is similar to the lattice Boltzmann method but which is based on F and avoids the high memory consumption in LBM which results from the necessity to store all occupation numbers. While the system (23) 24) and (25) is obtained by ....

P.A. Skordos. Initial and boundary conditions for the Lattice Boltzmann method. Phys. Rev. E, 48:4823--4842, 1993.

....is very important in practical situations. 1 Further, I demonstrate experimentally that the discretization error of the lattice Boltzmann method decreases quadratically with finer resolution both in space and in time. My results on the lattice Boltzmann method have been published in Skordos [48], and have helped to bring the lattice Boltzmann method from the physicists world to the engineer s world. Apart from the lattice Boltzmann method, I examine two different kinds of explicit finite difference methods. In chapter 4, I compare the lattice Boltzmann method against an incompressible ....

....nodes, which are used as boundary conditions for the lattice Boltzmann method on the other side of the grid. The scheme for a composite grid is as follows. Let us assume that lattice Boltzmann is used on a coarse grid at the left side. Going from left to right, there is a 5 In my earlier paper [48], I suggested that the density at a wall should be calculated as the average of the populations that bring fluid into the boundary node from inner nodes and other neighboring boundary nodes. Further numerical experiments, however, indicate that the average of the populations after bounce back, ....

[Article contains additional citation context not shown here]

P.A. Skordos. Initial and boundary conditions for the lattice Boltzmann method. Physical Review E, 48(6):4823--4842, December 1993.

....not relevant. Instead, explicit methods are preferable in this case because of their simplicity and ease of parallelization. In our system, we employ the following two explicit methods: explicit finite differences (Peyret Taylor [19] and the recently developed lattice Boltzmann method (Skordos [20]) The finite difference method is a straightforward discretization of the Navier Stokes equations 1 3. Specifically, the spatial derivatives are discretized using centered differences on a uniform orthogonal grid, and the time derivatives are discretized using forward Euler differences ....

.... steps for the lattice Boltzmann method is as follows, ffl Relax F i (inner) ffl Shift F i (inner) ffl Communicate: send recv F i (boundary) ffl Calculate ae; V x ; V y from F i (inner) ffl Filter ae; V x ; V y (inner) More details on the lattice Boltzmann method can be found in Skordos [20]. Regarding the communication of boundary values by the finite difference method (FD) and the lattice Boltzmann method (LB) there are some differences that will become important in the next two sections, when we discuss the performance of our parallel simulation system. The first difference is ....

[Article contains additional citation context not shown here]

P. Skordos, "Initial and boundary conditions for the lattice Boltzmann method," Physical Review E, vol. 48, no. 6, pp. 4823--4842, December 1993.

....the outlet, V (t) V final 1 Gamma 10 Gamma (t=T ) 2 (4) where T is 3 ms. 3. NUMERICAL METHODS The Navier Stokes equations are solved numerically using a uniform grid and two different explicit numerical methods: the lattice Boltzmann method and a traditional finite difference method [4, 5]. The simulation results obtained with the lattice Boltzmann method and the finite difference method are very similar to each other; and for the sake of brevity, only the lattice Boltzmann simulations are presented here. A fourth order artificial viscosity filter is used in combination with the ....

Skordos, P., "Initial and boundary conditions for the lattice Boltzmann method," Physical Review E, vol. 48, no. 6, pp. 4823--4842, (December 1993).

....flow at high Reynolds number. The same filter is used both for the finite difference method and for the lattice Boltzmann method. The lattice Boltzmann method is a recentlydeveloped method for simulating subsonic flow which is competitive with finite differences in terms of numerical accuracy [17, 15] and has slightly better stability properties. The lattice Boltzmann method uses two kinds of variables to represent the fluid: the traditional fluid variables ae; V x ; V y and another set of variables called populations F i . During each cycle of the computation, the fluid variables ae; V x ; V ....

....two dimensional problems, both methods communicate 3 variables per fluid node. 7 Performance measurements We measure the performance of the distributed system when using the finite difference method and the lattice Boltzmann method to simulate HagenPoiseuille flow through a rectangular channel [17]. The goal of testing both methods is to examine the performance of the parallel system on two similar, but slightly different parallel algorithms. It should be noted that the two methods produce comparable results for the same resolution, and that both methods converge quadratically with ....

P. Skordos, "Initial and boundary conditions for the lattice Boltzmann method," Physical Review E, vol. 48, no. 6, pp. 4823--4842, December 1993.

....as the size of the subregions increases. The poor per3 formance for very small subregions (abrupt drop in performance) is expected because the Ethernet network has high latency and a disproportionate cost for small messages. In these tests, the lattice Boltzmann numerical method (reference [5]) is used, which is a recently developed explicit method for subsonic compressible flow. Similar results are obtained using traditional finite difference methods. A detailed description of the numerical methods and the measurements can be found in reference [3] Figure 2: Parallel efficiency of 3D ....

P. Skordos, "Initial and boundary conditions for the lattice Boltzmann method," Physical Review E, vol. 48, no. 6, pp. 4823--4842, December 1993.

No context found.

P. A. Skordos, Initial and boundary conditions for the Lattice Boltzmann method, Phys. Rev. E 48 (1993), 4823-4842.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC