• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.243-259
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• 2016

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.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.695-708
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• 2024

In this paper we present a non-standard finite difference method for solving a fractional decay model. The proposed NSFDM is constructed by incorporating a non-standard denominator function, resulting in an explicit numerical scheme as easy as the conventional Euler method, but it provides very accurate solutions and has unconditional stability. Two examples from the literature are presented to demonstrate the performance of the proposed numerical scheme, which is compared to three methods from the literature. It is found that the method's estimated errors are extremely minimal, such as within the machine precision.

• 한국가시화정보학회:학술대회논문집
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• 2005.12a
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• pp.111-116
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• 2005

An automobile engine has the Positive Crankcase Ventilation system (PCV system) for preventing air pollution as the environmental problem is important In this system, a PCV valve is the most important component to control the flow rate of Blowby gas which is generated by various engine powers. But, in the working place, the design of a PCV valve is very difficult because of interaction between fluid and solid motions. In this study, we investigated fluid flow characteristics using re-meshing method of a CFD technique to simulate spool behavior. As the results, a spool is periodically oscillated with time and is largely oscillated in proportion to the differential pressure between inlet and outlet. And, although the velocity at the orifice increases with the differential pressure, the flow rate of the outlet decreases. This research may give PCV designers visual flow information to help them

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.295-309
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• 2023

The Richards' equation attracts the attention of several scientific researchers due to its importance in the hydrogeology field especially porous soil. This work presents a numerical method to solve the two dimensional Richards' equation. The pressure form and the mixed form of Richards' equation are solved numerically using a bivariate diamond finite volumes scheme. Euler explicit scheme is used for the time discretization. Different test cases are done to validate the accuracy and the efficiency of our numerical model and to compare the possible numerical strategies. We started with a first simple test case of Richards' pressure form where the hydraulic capacity and the hydraulic conductivity are taken constant and then a second test case where the hydrodynamics parameters are linear variables. Finally, a third test case where the soil parameters are taken according the Van Gunchten empirical model is presented.

• Geotechnical Engineering
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• v.14 no.4
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• pp.129-140
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• 1998

Elasto-plastic finite element analysis of geotechnical boundary value problems necessitate the stress integration for the known strain increments. For the elasto-plastic constitutive model, the stress integration is generally achieved by numerical schemes, because analytical integration is impossible for general strain path. In this case, the accuracy of numerical stress integration has an important role on the overall accuracy of nonlinear finite element solution. In this study, the Sloan's substepping method which is one of explicit integration methods has been adopted and iris applicability has been checked. The unstability and inaccuracy of ifs results initiated from initial stress level were revealed. So. a new modified numerical integration method which employs the basic concept of modified Euler scheme for error control is proposed and accuracy and stability of the solutions are confirmed by triaxial test simulation.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.223-227
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• 2005

A PCV valve is a part to control the flow rate of Blowby gas in a PCV system. A PCV system re-burns Blowby gas with fuel in a combustion chamber. Some gas enters to a crankcase room through the gap between piston ring and engine cylinder wall. This gas si called 'Blowby gas'. This gas causes many problems. In environmental view, Blowby gas includes about $25\~35\%$ hydrocarbon{HC) of total generated HC in an automobile. Hydrocarbon is a very harmful pollutant element in our life. In mechanical view, Blowby gas has some reaction with lubricant oil of crankcase room. Then, this causes lubricant oil contamination, crankcase corrosion and a decrease fo engine efficiency. Consequently, Blowby gas must be eliminated from a crankcase room. In this study, we simulated internal flow characteristics in a PCV valve according to spool dynamic behavior using local remeshing method And, we programmed our sub routine to simulate a spool dynamic motion. As results, spool dynamic behavior is periodically oscillated by the relationship between fluid force and elastic force of spring. And its magnitude is linearly increased by the differential pressure between inlet and outlet. Also, as spool is largely moved, flow area is suddenly decreased at orifice. For this reason, flow velocity is rapidly decreased by viscous effect.