International Journal of Numerical Methods for Heat & Fluid Flow

Purpose – This paper seeks to develop an adaptive finite volume algorithm, and to present an extensive numerical analysis of it.

Design/methodology/approach – The effectiveness of the developed algorithm is demonstrated through practical and computationally challenging problems. The algorithm is tested for a wide range of singularities.

Findings – The convergence of the presented algorithm is independent of the regularity of the problems. It is shown that the our algorithm produces more accurate and well conditioned matrix systems.

Research limitations/implications – Though the presented algorithm works for extreme singularities on rectangular meshes, it may not be as efficient if the underlying meshes are distorted, and it may not converge. Further research is under way for including the multi-point approximation technique into the algorithm.

Practical implications – Almost all reservoir simulators use the two-point method, and this algorithm is based on this method. The algorithm can be easily incorporated into the reservoir simulators. The results show that such an implementation will greatly improve the computational efficiency of the simulators. The work is useful for computational scientists, and especially for the researchers in oil industries. The paper reports the numerical work with practical applications.

Originality/value – The paper develops an adaptive finite volume algorithm. It is shown that adaptive meshes represent the underlying problem more accurately, and matrix systems associated with adaptive meshes are easier to solve compared with matrix systems associated with uniform meshes.