Construction of analytical solutions and numerical methods comparison of the ideal continuous settling model

• Analytical solutions of the ideal continuous settling model are constructed based on the Method of Characteristics.
• The analytical solutions were compared with experimental data to show accuracy.
• Three numerical methods converge to the MOC solution with varying efficiency.
• A basis for technique selection based upon the accuracy, computing and coding complexity is shown.

Continuous sediment has a wide application in chemical engineering process, such as wastewater treatment, water reuse, mineral waste manage and processing. This paper provides analytical solutions of the ideal continuous settling model by using the method of characteristics. The analytical solutions are compared with experiment data to show that the solutions accurately predict the sediment height and concentration as a function of time and loading conditions. Additionally, three alternative methods, using finite differences are compared to the analytical solutions, and their accuracy and efficiency are evaluated. It is shown that all three methods are reliable for solving sedimentation problems but have varying efficiency. Method YRD is the most accurate but also has the greatest computation and implementation cost. Method SG is the least accurate but is the easiest to implement with lowest computation cost. Method G is a compromise between the two methods, providing acceptable accuracy and low computation cost.