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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.20 No.3
- 발행연도
- 2016.9
- 수록면
- 243 - 259 (17page)
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The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.
목차
ABSTRACT
1. INTRODUCTION
2. GOVERNING EQUATION AND DISCRETIZATION
3. ITERATIVE METHODS
4. NUMERICAL SIMULATIONS
5. RESULTS AND DISCUSSIONS
6. CONCLUSION
REFERENCES
참고문헌 (36)
참고문헌 신청
[단행본] - H. F.Wang / 1982 / Introduction to Groundwater Modeling: Finite Difference and Finite Element Methods / Freeman
[단행본] - C. Zheng / 1995 / Applied Contaminant Transport Modeling: Theory and Practice / Van Nostrand Reinhold
[학술지(정기간행물)] - R. L. Cooley / 1983 / Some new procedures for numerical solution of variably saturated flow problems / Water Resour. Res 19 : 1271 ~ 1285
[학술지(정기간행물)] - S. P. Neuman / 1973 / Saturated-unsaturated seepage by finite elements / J. Hydraul. Div. ASCE 99 : 2233 ~ 2250
[학술지(정기간행물)] - P. C. D. Milly / 1985 / A mass-conservative procedures for time-stepping in models of unsaturated flow / Adv. Water Resources 8 : 32 ~ 36
[단행본] - C. Zheng / 1995 / Applied Contaminant Transport Modeling: Theory and Practice / Van Nostrand Reinhold
[학술지(정기간행물)] - R. L. Cooley / 1983 / Some new procedures for numerical solution of variably saturated flow problems / Water Resour. Res 19 : 1271 ~ 1285
[학술지(정기간행물)] - S. P. Neuman / 1973 / Saturated-unsaturated seepage by finite elements / J. Hydraul. Div. ASCE 99 : 2233 ~ 2250
[학술지(정기간행물)] - P. C. D. Milly / 1985 / A mass-conservative procedures for time-stepping in models of unsaturated flow / Adv. Water Resources 8 : 32 ~ 36
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UCI(KEPA) : I410-ECN-0101-2017-410-001102260