FASTEST - A new high order FV method dynamically locally self h-adaptive for convective-diffusive problems

In this article a new finite volume method for the numerical solution of convective-diffusive 1D problems is developed. It is conservative, high order in time and space, allows the partitioning of the domain by equal or unequal finite volumes, thus dynamically locally self h-adaptive. The definition of the monotonic profiles is accomplished by means of cubic weighted ν -splines and Taylor expansions. The profile analysis is conducted in the normalized plane with the velocity varying in time and space. Moreover the flux is assigned by Upwind or by second order back-ward Characteristics if the estimated flux is outside of the unit square or the transformation into the normalized plane is not possible, respectively. The formulation of dynamically locally self h-adaptive processes is designed to achieve the dual purpose to increase the accuracy and to keep as small as possible the number of finite volumes. The initial-boundary stability and convergence properties of the new method are examined in detail, also in presence of h-adaptivity. In addition, a generalization of the new scheme to 2D and 3D problems is presented. Finally, some numerical test are carried out to verify the properties of the new method, including two CFD problems. Mathematics Subject Classification: 65M08, 65M12, 65N08, 65N12, 65N22, 65N50, 76M12