TY - JOUR
T1 - An efficient bound-preserving and energy stable algorithm for compressible gas flow in porous media
AU - Kou, Jisheng
AU - Wang, Xiuhua
AU - Chen, Huangxin
AU - Sun, Shuyu
N1 - KAUST Repository Item: Exported on 2022-11-14
Acknowledgements: The work of Xiuhua Wang was supported by the Scientific and Technical Research Project of Hubei Provincial Department of Education (No. D20192703). The work of Huangxin Chen was supported by the NSF of China (Grant No. 12122115, 11771363).
PY - 2022/11/11
Y1 - 2022/11/11
N2 - Due to the great significance of the natural gas and shale gas, it is becoming increasingly important to simulate compressible gas flow in porous media. The model obeys an energy dissipation law as well as molar density must be positive and bounded in terms of the equation of state. For the purpose of eliminating nonphysical solutions as well as improving the stability in practical simulation, preservation of these properties is essential for a promising numerical method, but it is actually challenging due to the strong nonlinearity and complexity of the model. In this paper, we propose an efficient linearized numerical scheme that inherits the energy dissipation law as well as preserves the boundedness of molar density. Specifically, to treat the logarithmic type Helmholtz free energy density determined by the Peng-Robinson equation of state, we propose a novel adaptive stabilization approach involving the second derivatives of the convex energy terms. At each time step, the stabilization parameter is adaptively updated by a simple and explicit formula to ensure the energy dissipation law. The stabilized and linearized chemical potential allows to formulate the local mass conservation equation as an equivalent convection-diffusion form, and from this, an adaptive time step strategy is proposed to preserve the positivity and boundedness of molar density. The calculation of the time step size is fully explicit and easy to implement. Additionally, the fully discrete scheme is constructed using the conservative cell-centered finite difference method with the upwind strategy, and thus, it enjoys the local mass conservation. Numerical results are also presented to demonstrate the excellent performance of the proposed scheme.
AB - Due to the great significance of the natural gas and shale gas, it is becoming increasingly important to simulate compressible gas flow in porous media. The model obeys an energy dissipation law as well as molar density must be positive and bounded in terms of the equation of state. For the purpose of eliminating nonphysical solutions as well as improving the stability in practical simulation, preservation of these properties is essential for a promising numerical method, but it is actually challenging due to the strong nonlinearity and complexity of the model. In this paper, we propose an efficient linearized numerical scheme that inherits the energy dissipation law as well as preserves the boundedness of molar density. Specifically, to treat the logarithmic type Helmholtz free energy density determined by the Peng-Robinson equation of state, we propose a novel adaptive stabilization approach involving the second derivatives of the convex energy terms. At each time step, the stabilization parameter is adaptively updated by a simple and explicit formula to ensure the energy dissipation law. The stabilized and linearized chemical potential allows to formulate the local mass conservation equation as an equivalent convection-diffusion form, and from this, an adaptive time step strategy is proposed to preserve the positivity and boundedness of molar density. The calculation of the time step size is fully explicit and easy to implement. Additionally, the fully discrete scheme is constructed using the conservative cell-centered finite difference method with the upwind strategy, and thus, it enjoys the local mass conservation. Numerical results are also presented to demonstrate the excellent performance of the proposed scheme.
UR - http://hdl.handle.net/10754/685650
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021999122008142
U2 - 10.1016/j.jcp.2022.111751
DO - 10.1016/j.jcp.2022.111751
M3 - Article
SN - 0021-9991
SP - 111751
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -