We present a finite-volume formulation for the lattice Boltzmann method (FVLBM) based on standard bilinear quadrilateral elements in two dimensions. The accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the Navier-Stokes equations for time dependent rotating Couette flow and Taylor vortex flow. To demonstrate the flexibility of the scheme, w...

We introduce and study finite d-volumes the high dimensional generalization of finite metric spaces. Having developed a suitable combinatorial machinery, we define l1-volumes and show that they contain Euclidean volumes and hypertree volumes. We show that they can approximate any d-volume with O(n) multiplicative distortion. On the other hand, contrary to Bourgain’s theorem for d = 1, there exi...