The Extension of Convective Boundedness Criterion

Tie paper describes an extension of the well-known Convective Boundedness Criterion (CBC). It is shown that the newly proposed criterion is a combination of the CBC and the extended convective boundedness criterion (ECBC), as shown in Fig.]. A new scheme (NECBC1) based on the new criterion is designed and tested by two problems: (1) convection of a stepwise profile in an oblique uniform velocity field and (2) convection of an elliptical profile in a stagnation point flow. The numerical tests show the effectiveness of the new criterion and reveal the limitation of the CBC and the ECBC. Moreover, some numerical experiments of some specially-designed schemes and two TVD-Type schemes: the van Albada scheme and Miroslav Cada & Manuel Torrilhon's new third-order scheme, are carried out. Through these numerical experiments, some extra constraints for the new criterion are observed and in the meantime some other possible regions in the normalized diagram (NV) for high-resolution schemes reveal themselves.