We propose an a-posteriori error/smoothness indicator for standard semidiscrete finite volume schemes for systems of conservation laws,based on the numerical production of entropy.This idea extends previous work by th...We propose an a-posteriori error/smoothness indicator for standard semidiscrete finite volume schemes for systems of conservation laws,based on the numerical production of entropy.This idea extends previous work by the first author limited to central finite volume schemes on staggered grids.We prove that the indicator converges to zero with the same rate of the error of the underlying numerical scheme on smooth flows under grid refinement.We construct and test an adaptive scheme for systems of equations in which the mesh is driven by the entropy indicator.The adaptive scheme uses a single nonuniform grid with a variable timestep.We show how to implement a second order scheme on such a space-time non uniform grid,preserving accuracy and conservation properties.We also give an example of a p-adaptive strategy.展开更多
In this work we present a family of relaxation schemes for nonlinear convection diffusion problems,which can tackle also the cases of degenerate diffusion and of convection dominated regimes.The schemes proposed can a...In this work we present a family of relaxation schemes for nonlinear convection diffusion problems,which can tackle also the cases of degenerate diffusion and of convection dominated regimes.The schemes proposed can achieve any order of accuracy,give non-oscillatory solutions even in the presence of singularities and their structure depends only weakly on the particular PDE being integrated.One and two dimensional results are shown,and a nonlinear stability estimate is given.展开更多
文摘We propose an a-posteriori error/smoothness indicator for standard semidiscrete finite volume schemes for systems of conservation laws,based on the numerical production of entropy.This idea extends previous work by the first author limited to central finite volume schemes on staggered grids.We prove that the indicator converges to zero with the same rate of the error of the underlying numerical scheme on smooth flows under grid refinement.We construct and test an adaptive scheme for systems of equations in which the mesh is driven by the entropy indicator.The adaptive scheme uses a single nonuniform grid with a variable timestep.We show how to implement a second order scheme on such a space-time non uniform grid,preserving accuracy and conservation properties.We also give an example of a p-adaptive strategy.
基金This work was supported by MIUR/PRIN2005 project“Modellistica numerica per il cal-colo scientifico ed applicazioni avanzate”.
文摘In this work we present a family of relaxation schemes for nonlinear convection diffusion problems,which can tackle also the cases of degenerate diffusion and of convection dominated regimes.The schemes proposed can achieve any order of accuracy,give non-oscillatory solutions even in the presence of singularities and their structure depends only weakly on the particular PDE being integrated.One and two dimensional results are shown,and a nonlinear stability estimate is given.
