Improved second-order hyperbolic residual-distribution scheme and its extension to third-order on arbitrary triangular grids

摘要: In this paper, we construct second- and third-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the accuracy of second-order in J. Comput. Phys. 227 (2007) 315-352 229 (2010) 3989-4016 can be greatly improved by requiring scheme to preserve exact quadratic solutions. The easily extended a further exactness cubic These are constructed based SUPG methodology formulated framework method, thus considered as economical powerful alternatives high-order finite-element methods. For both schemes, fully implicit solver residual Jacobian proposed scheme, rapid convergence, typically with no more than 10-15 Newton iterations (and about 200-800 linear relaxations per iteration), reduce residuals ten orders magnitude. also these separate treatment advective diffusive terms, which paves way construction compressible Navier-Stokes equations. Numerical results show produce exceptionally accurate smooth solution gradients highly skewed anisotropic grids even curved boundary problem, without introducing elements. A reconstruction normals integration technique boundaries provided details.