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Abstract

Various cases of scalar convection-dominated equation have been investigated by lots of researchers not only for its applications in many engineering problems, but also as test cases to improve the understanding in the other two aspects; firstly, in the testing of a numerical scheme, and secondly, in the analysis of numerical issues in the solution itself. In this paper, we consider the last aspect. In particular, we investigate the cases involving different Dirichlet boundary conditions when the scalar convection-dominated flow is steady, as well as transient flow. Such investigation focuses on spurious oscillation in the solution of the equation. The oscillation is first modelled by means of Fourier series. Then we take a closer look into the oscillation’s characteristics in each individual case. We show that some of the characteristics is inherent in each case. The criteria to avoid such oscillation is verified against the solution itself, and some apparent anomalies are identified.