High-order monotonicity-preserving compact schemes for linear scalar advection on 2-D irregular meshes

This paper is concerned with the numerical solution for linear scalar advection problems, the velocity field of which may be uniform or a given function of the space variable. We would like to propose the following: (1) a new family of I-D compact explicit schemes, which preserve monotonicity while maintaining high-order accuracy in smooth regions and (2) an extension to the 2-D case of this family of schemes. which ensures good accuracy and isotropy of the computed solution even for very distorted meshes. A few theoretical results are proven, while abundant numerical tests are shown in order to illustrate the quality of the schemes at issue. (C) 2002 Elsevier Science (USA).