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A variable relaxation scheme for multiphase, multicomponent flow

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Abstract

We propose a variable relaxation scheme for the simulation of 1D, two-phase, multicomponent flow in porous media. For these strongly nonlinear systems, traditional high order upwind schemes are impractical: Riemann solutions are not directly available when the phase behavior is complex, and the systems are weakly hyperbolic at isolated points. Relaxation schemes avoid the dependency on the eigenstructure and nonlinear Riemann solvers by approximating the original system with a strongly hyperbolic linear system. We exploit the known information about the eigenvalues to construct first order and second order variable relaxation schemes with much reduced numerical diffusion as compared to the standard relaxation formulations. The proposed second order variable relaxation scheme is competitive in accuracy and efficiency with a third order component-wise ENO reconstruction, and performs at least as well as second order component-wise TVD schemes.

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Correspondence to Shalini B. Krishnamurthy.

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Krishnamurthy, S.B., Gerritsen, M.G. A variable relaxation scheme for multiphase, multicomponent flow. Transp Porous Med 71, 345–377 (2008). https://doi.org/10.1007/s11242-007-9130-7

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Keywords

  • Multicomponent
  • multiphase flows
  • Miscible displacement
  • Weak hyperbolicity
  • Relaxation schemes
  • Gas injection