In:
Mathematical Modelling and Analysis, Vilnius Gediminas Technical University, Vol. 8, No. 2 ( 2003-06-30), p. 113-120
Abstract:
The goal of the paper is to present and test the nonlinear monotonization of the Babenko scheme for solving 2D linear advection equation with alternating‐sign velocities. The numerical method of monotonization is based on the idea of limited artificial diffusion. There are some approaches for constructing quasi‐monotonic second order approximation schemes for solving hyperbolic systems and equations of gas dynamics: flux correction methods, the Godunov method, TVD methods and others. In particular, many authors developed the idea of TVD method. We try to use this idea to get a new quasi‐monotonic high order accuracy scheme based on the well‐known non‐monotonic Babenko scheme. The algorithm is presented for 1D problem. For testing 2D problem we use the splitting algorithm. The proposed monotonized scheme has shown the best results among all considered in the paper schemes especially for non-smooth initial profile.
Type of Medium:
Online Resource
ISSN:
1392-6292
,
1648-3510
DOI:
10.3846/13926292.2003.9637216
Language:
Unknown
Publisher:
Vilnius Gediminas Technical University
Publication Date:
2003
detail.hit.zdb_id:
2578803-6
SSG:
11
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