Application of Advanced Numerical Methods to Solve the Batch Sedimentation Problem: Tangent of Hyperbola Interface Capturing, Weighted Essentially Non-Oscillatory and High-Resolution Central Scheme

The numerical solution of the sedimentation phenomenon presents a significant challenge due to the presence of discontinuities at interfaces, characterized by three distinct regions: (i) clear liquid, (ii) constant solid concentration, and (iii) solid concentration varying from the initial to a maximum value. This problem is particularly relevant in the oil industry, where sedimentation is an essential unit operation in processes such as wastewater treatment, drilling fluid control, and phase separation during production. Discontinuities and abrupt variations in solid concentrations pose significant challenges for traditional numerical methods in solving this model type. In this study, three high-order numerical methods (Tangent of Hyperbola Interface Capturing, Weighted Essentially Non-Oscillatory, and High-Resolution Central Scheme) are employed to solve two classic case studies in the sedimentation process. In general, the results indicate that all three methods were effective in handling the discontinuities at the phase interfaces while maintaining the accuracy and stability of the solution. Moreover, although all methods performed satisfactorily in various aspects, the High-Resolution Central Scheme was found to be the most efficient in terms of computational time.