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The Navier-Stokes equations with variable density are challenging problems in numerical analysis community. We recently built the 2nd order stabilized Gauge-Uzawa method [SGUM] to solve the Navier-Stokes equations with constant density and have estimated theoretically optimal accuracy. Also we proved that SGUM is unconditionally stable. In this paper, we apply SGUM to the Navier-Stokes equations with nonconstant variable density and find out the stability condition of the algorithms. Because the condition is rather strong to apply to real problems, we consider Allen-Cahn scheme to construct unconditionally stable scheme.
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참고문헌 (19)
참고문헌 신청
S.M. Allen / 1979 / A microscopic theory for antiphase boundary mo-tion and its application to antiphase domain coarsening / Acta Metallurgica 27:1085~1095
Alexandre Ern / 2004 / Theory and practice of finite elements / Applied Mathematical Scioences 159
J.-L. Guermond / 2000 / A projection FEM for variable density in-compressible ows / J. comput. Phys 165:167~188
J.-.L. Guermond / 2009 / A spliiting method for incompressible ows with variable density based on a pressure Poisson equation / J. comput. Phys 228:2834~2846
J.-.L. Guermond / 2011 / Error analysis of a fractional time-stepping technique for incompressible ows with variable density / SIAM J. Numer. Anal. 49:917~944
Alexandre Ern / 2004 / Theory and practice of finite elements / Applied Mathematical Scioences 159
J.-L. Guermond / 2000 / A projection FEM for variable density in-compressible ows / J. comput. Phys 165:167~188
J.-.L. Guermond / 2009 / A spliiting method for incompressible ows with variable density based on a pressure Poisson equation / J. comput. Phys 228:2834~2846
J.-.L. Guermond / 2011 / Error analysis of a fractional time-stepping technique for incompressible ows with variable density / SIAM J. Numer. Anal. 49:917~944
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