Condition for Non-Oscillatory Solution for Scalar ConvectionDominated Equation

Abstract

The scalar convection-dominated flows are found in different science and designing applications which incorporates those concerning the computational fluid dynamics problems of mesh structure in the numerical estimations. These flows are thus essential in nature. Despite the fact that these types of flow have been widely discussed among fluid dynamists, the contribution of mesh and flow parameters in predicting spurious-oscillation free solutions remains unclear. In this research, the significance of the connections between the mesh structure and the scalar convection-dominated flow parameters is accentuated. A systematic technique is applied in the setting of the parameters of interest. In particular, we present the a priori formulation of condition to avoid spurious oscillatory solutions, which depends on both Peclet number as well as the number of grid. The condition is useful in a more efficient decision-making in the selection of the computational domain grid, and in eradicating some heuristic parts of the scalar concentration estimate. The results of the test case affirm the consistency of the condition. It is found that, given the right constant value in the amplification factor term within the spatial error growth model, the condition is able to capture the presence of kinks which mark the beginning of the oscillations.