In the present paper, a new difference matrix via difference operator D is introduced. Let x = (xk) be a sequence of real numbers, then the difference operatorD is defined by D(x)n =∑kn=0(-1)k(n-kn)xk,where ...In the present paper, a new difference matrix via difference operator D is introduced. Let x = (xk) be a sequence of real numbers, then the difference operatorD is defined by D(x)n =∑kn=0(-1)k(n-kn)xk,where n = 0,1,2,3,.... Several interestingproperties of the new operator D are discussed.展开更多
We propose to extend the d’Humi`eres version of the lattice Boltzmann scheme to triangular meshes.We use Bravais lattices or more general lattices with the property that the degree of each internal vertex is supposed...We propose to extend the d’Humi`eres version of the lattice Boltzmann scheme to triangular meshes.We use Bravais lattices or more general lattices with the property that the degree of each internal vertex is supposed to be constant.On such meshes,it is possible to define the lattice Boltzmann scheme as a discrete particle method,without need of finite volume formulation or Delaunay-Voronoi hypothesis for the lattice.We test this idea for the heat equation and perform an asymptotic analysis with the Taylor expansion method for two schemes named D2T4 and D2T7.The results show a convergence up to second order accuracy and set new questions concerning a possible super-convergence.展开更多
文摘In the present paper, a new difference matrix via difference operator D is introduced. Let x = (xk) be a sequence of real numbers, then the difference operatorD is defined by D(x)n =∑kn=0(-1)k(n-kn)xk,where n = 0,1,2,3,.... Several interestingproperties of the new operator D are discussed.
基金the“LaBS project”(Lattice Boltzmann Solver,www.labs-project.org)funded by the French“FUI8 research program”。
文摘We propose to extend the d’Humi`eres version of the lattice Boltzmann scheme to triangular meshes.We use Bravais lattices or more general lattices with the property that the degree of each internal vertex is supposed to be constant.On such meshes,it is possible to define the lattice Boltzmann scheme as a discrete particle method,without need of finite volume formulation or Delaunay-Voronoi hypothesis for the lattice.We test this idea for the heat equation and perform an asymptotic analysis with the Taylor expansion method for two schemes named D2T4 and D2T7.The results show a convergence up to second order accuracy and set new questions concerning a possible super-convergence.