TY - JOUR

T1 - Application of Adomian Decomposition Method to Bounded and Unbounded Stokes' Problems

AU - Liu, Chi Min

AU - Yang, Ray Yeng

N1 - Funding Information:
Financial support from the Ministry of Science and Technology of Taiwan with the grants MOST 106-2221-E-270-002-MY2, MOST 106-2911-I-006-301, and MOST 107-3113-E-006-004-CC2 is acknowledged.
Publisher Copyright:
© 2018 Chi-Min Liu and Ray-Yeng Yang.

PY - 2018

Y1 - 2018

N2 - The well-known Stokes' problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes' problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes' problems of finite and infinite depths.

AB - The well-known Stokes' problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes' problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes' problems of finite and infinite depths.

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U2 - 10.1155/2018/5693276

DO - 10.1155/2018/5693276

M3 - Article

AN - SCOPUS:85058811275

VL - 2018

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

M1 - 5693276

ER -