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.
Wide range of mesh types are proposed in computational fluid dynamics which in turn initiate further discussions over problems of their structure in the numerical computation of fluid flows. Nevertheless, such discussions might sometimes lead to illfitted choices of mesh for specific problem. Some types, if improperly used, can cause spurious oscillation in the solutions of governing equations. Furthermore, the contribution of mesh and flow parameters in predicting spurious oscillation free solutions has been much-debated topic over the last decades. Comparison was made in this research between uniform and piecewise-uniform meshes in accentuating the significance of the mesh structure and singular perturbation parameter connection in numerical solution of a singularly perturbed problem. A systematic technique was particularly applied in setting both the singular perturbation parameter and mesh number. Based on the a priori formulation, the condition to avoid spurious oscillatory solutions on the two types of mesh which depends on the parameters of interest is presented in this paper. This was done by adopting reasonable mesh interval sizes. The results of the test cases affirmed the consistency of the condition. It becomes clear that, in general both parameters of interest are linearly related in each case, and the piecewise-uniform mesh number is doubled that of the uniform mesh in order to obtain realistic solution.
There is a considerable discussion in computational fluid dynamics over the mesh structure problems for the numerical computation. Due to wide range of mesh schemes proposed by fluid dynamists, there is sometimes confusion over the correct scheme for certain problem. Furthermore, some schemes, if improperly used, can lead to nonphysical solution. We emphasize in this paper the importance of the mesh structure and singular perturbation parameter relationship in numerical solution of a singularly perturbed two-point boundary value problem. Based on the perturbation parameter, we particularly suggest a systematic technique in setting the mesh number. This is done by adopting mesh of Shishkin type. It becomes clear that the parameters of interest are linearly related. Since it is necessary to have a decision-making that is more structured, and reduce heuristic error in mesh of computational domain determination, such relationship serves as a guideline for the numerical solution of a singularly perturbed problem that is physically correct.
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