A CONSERVATIVE MESH-FREE SCHEME AND GENERALIZED FRAMEWORK FOR CONSERVATION LAWS

作者：Chiu Edmond Kwan Yu^*; Wang Qiqi; Hu Rui; Jameson Antony

来源：SIAM Journal on Scientific Computing, 2012, 34(6): A2896-A2916.

DOI：10.1137/110842740

• conservation law
• advection equation
• mesh-free scheme
• finite difference
• finite volume

We present a novel mesh-free scheme for solving partial differential equations. We first derive a conservative and stable formulation of mesh-free first derivatives. We then show that this formulation is a special case of a general conservative mesh-free framework that allows flexible choices of flux schemes. Necessary conditions and algorithms for calculating the coefficients for our mesh-free schemes that satisfy these conditions are also discussed. We include numerical examples of solving the one-and two-dimensional inviscid advection equations, demonstrating the stability and convergence of our scheme and the potential of using the general mesh-free framework to extend finite volume discretization to a mesh-free context.

• 出版日期2012