Numerical Reservoir Solution

 This is a coding program for my Numerical Reservoir Simulation course which can be counted as a bahcelor's and master's class simultaneously. It aims to solve a problem of the numerical reservoir simulation and we need to see some changes or behavoirs of the reservoir fluid characteristic. The finite volume method and the finite difference method are used to calculate governing equation with the given parameters below.

Equation:  ∂c/∂t + ∇*(νc) = 0

Velocity Constant :  ν = 0.05 , m/s

Unit Area : A = 1 , m2

Domain: [0;1]

Size of Cell : dx = 0.1 , m

Time Step : dt = 0.1 , s

Simulation Time: n = 60 steps,   total time T = 6, s

Boundary Condition: c=1 at x=0,  c=0 at x=1


We examine the given conditions and parameters. We need to find different graphs outputs are shown from below figures:

- Finite Volume Method: Explicit in time, Central difference method in space. 

- Finite Difference Method: Explicit in time, Central difference method in space. 

- Finite Volume Method: Explicit in time, Upwinding method in space. 

- Finite Difference Method: Explicit in time, Upwinding method in space.



   Figure 1: Finite Difference Method, upwinding in space



Figure 2:  Finite Difference Method, central difference in space



Figure 3: Finite Volume Method, upwinding in space



Figure 4: Finite Volume Method, central difference in space

Location: Üniversiteler, Dumlupınar Blv. 1/6 D:133, 06800 Çankaya/Ankara, Türkiye

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