Condition for Non-Oscillatory Solution for Scalar Convection-Dominated 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 convectiondominated 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.

Comparative Study of the Condition for Non-Oscillatory Solution of a Singularly Perturbed Problem on Uniform and Piecewise-Uniform Meshes

“…Interestingly to note that the condition as given in Eq. (21) is applicable not only for the solution on a uniform mesh as discussed in a study by Aslam [28], but also a piecewise-uniform mesh; it gives the values of below which non-physical solutions occur. The solution on the uniform mesh reflects that the linear relationship between both parameters of interest (i.e.…”

“…3is examined in connection with mesh number . The work is an extension to that on mesh and low Peclet numbers' relationship that was discussed in previous studies [28,29]. Since the solutions are at the risk of being nonphysical, the reduction of mesh number needs to be done with care.…”

Relationship between Mesh Number and Singular Perturbation Parameter for the Solution of Singularly Perturbed Two-Point Boundary Value Problem

“…3in connection with mesh number . The work is an extension to that of mesh and low Peclet numbers' relationship that was discussed in Abdullah [28][29]'s studies. Since the solutions are at the risk of being nonphysical, the reduction of mesh number needs to be done with care.…”