An OpenMP parallel godunov scheme for 1D two phase oil displacement problem

Water flooding can be governed by Buckley-Leverett equation. Its analytic solution is constructed by following its characteristic curve. Whereas the numerical solution is approached using Godunov scheme. The computational results are shown in a good agreement with the analytic solution. The solutions consist of both shock and rarefaction waves. In the results, the amount of oil will be pushed by the water flow through the production well followed by a mix region of the fluids. To reduce computational cost, in this research, the OpenMP parallel programming is used. Moreover, using the parallel algorithm the speedup and efficiency are obtained 2.79 and 69.8% respectively with the number of grids 5 × 10
¹⁰
.