High-Order Monotonicity-Preserving Compact Schemes for Linear Scalar Advection on 2-D Irregular Meshes
✍ Scribed by Quang Huy Tran; Bruno Scheurer
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 560 KB
- Volume
- 175
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
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 1-D compact explicit schemes, which preserve monotonicity while maintaining highorder 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.