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We develop an entropy stable two-phase incompressible Navier--Stokes/Cahn--Hilliard discontinuous Galerkin (DG) flow solver method. ... stable approximation with an exact Riemann solver for advection and interface stabilization added to the BR1 method. ... Acknowledgements The authors would like to thank Dr. Gustaaf Jacobs of the San Diego State University for his hospitality. ...arXiv:1910.11252v2 fatcat:bsrtdnouojgcxduw6t3l2z6a34