Accurate Solutions of Rayleigh-Bénard Convection in Confined Two-Layer Systems Using the Spectral Domain Decomposition Method

REFERENCES

• E. Hewitt and R. Hewitt , The Gibbs–Wilbraham Phenomenon: An EPISODE in Fourier analysis , Archive for History of Exact Sciences , vol. 21 , no. 2 , pp. 129 – 160 , 1979 .
   Web of Science ®Google Scholar
• D. Gottlieb and C. Shu , On the Gibbs Phenomenon and Its Resolution , SIAM Rev. , pp. 644 – 668 , 1997 .
   Web of Science ®Google Scholar
• A. Gelb and E. Tadmor , Enhanced Spectral Viscosity Approximations for Conservation Laws , Appl. Numer. Math. , vol. 33 , no. 1 , pp. 3 – 22 , 2000 .
   Web of Science ®Google Scholar
• S. Osher and J. Sethian , Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton–Jacobi Formulations , J. Comput. Phys. , vol. 79 , no. 1 , pp. 12 – 49 , 1988 .
   Web of Science ®Google Scholar
• M. Sussman and M. Hussaini , A Discontinuous Spectral Element Method for the Level Set Equation , J. Sci. Comput. , vol. 19 , no. 1 , pp. 479 – 500 , 2003 .
   Web of Science ®Google Scholar
• H. Touil , M. Hussaini , and M. Sussman , Tracking Discontinuities in Hyperbolic Conservation Laws with Spectral Accuracy , J. Comput. Phys. , vol. 225 , no. 2 , pp. 1810 – 1826 , 2007 .
   Web of Science ®Google Scholar
• E. Marchandise , J. Remacle , and N. Chevaugeon , A Quadrature-Free Discontinuous Galerkin Method for the Level Set Equation , J. Comput. Phys. , vol. 212 , no. 1 , pp. 338 – 357 , 2006 .
   Web of Science ®Google Scholar
• E. Marchandise and J. Remacle , A Stabilized Finite Element Method Using a Discontinuous Level Set Approach for Solving Two Phase Incompressible Flows , J. Comput. Phys. , vol. 219 , no. 2 , pp. 780 – 800 , 2006 .
   Web of Science ®Google Scholar
• O. Desjardins and H. Pitsch , A Spectrally Refined Interface Approach for Simulating Multiphase Flows, J. Comput. Phys. , vol. 228, no. 5, pp. 1658–1677, 2009.
   Web of Science ®Google Scholar
• E. Marchandise , P. Geuzaine , N. Chevaugeon , and J. Remacle , A Stabilized Finite Element Method Using a Discontinuous Level Set Approach for the Computation of Bubble Dynamics , J. Comput. Phys. , vol. 225 , no. 1 , pp. 949 – 974 , 2007 .
   Web of Science ®Google Scholar
• S. V. Diwakar , S. K. Das , and T. Sundararajan , A Quadratic Spline Based Interface (QUASI) Reconstruction Algorithm for Accurate Tracking of Two-Phase Flows , J. Comput. Phys. , vol. 228 , no. 24 , pp. 9107 – 9130 , 2009 .
   Web of Science ®Google Scholar
• M. Hussaini , D. Kopriva , M. Salas , and T. Zang , Spectral Methods for the Euler Equations. II: Chebyshev Methods and Shock Fitting , AIAA J. , vol. 23 , no. 2 , pp. 234 – 240 , 1985 .
   Google Scholar
• S. Dennis and L. Quartapelle , Direct Solution of the Vorticity-Stream Function Ordinary Differential Equations by a Chebyshev Approximation , J. Comput. Phys. , vol. 52 , no. 3 , pp. 448 – 463 , 1983 .
   Web of Science ®Google Scholar
• A. Chorin , Numerical Solution of the Navier–Stokes Equations , Math. Comp , vol. 22 , no. 104 , pp. 745 – 762 , 1968 .
   Web of Science ®Google Scholar
• O. Botella , On the Solution of the Navier–Stokes Equations Using Chebyshev Projection Schemes with Third-Order Accuracy in Time , Comput. Fluids , vol. 26 , no. 2 , pp. 107 – 116 , 1997 .
   Web of Science ®Google Scholar
• R. Peyret , Spectral Methods for Incompressible Viscous Flow , vol. 148 , Springer-Verlag , Berlin , 2002 .
   Google Scholar
• C. Sabbah and R. Pasquetti , A Divergence-Free Multidomain Spectral Solver of the Navier–Stokes Equations in Geometries of High Aspect Ratio , J. Comput. Phys. , vol. 139 , no. 2 , pp. 359 – 379 , 1998 .
   Web of Science ®Google Scholar
• D. Johnson and R. Narayanan , Geometric Effects on Convective Coupling and Interfacial Structures in Bilayer Convection , Phys. Rev. E , vol. 56 , no. 5 , pp. 5462 – 5472 , 1997 .
   Web of Science ®Google Scholar
• A. Nepomnyashchy and I. Simanovskii , Influence of Thermocapillary Effect and Interfacial Heat Release on Convective Oscillations in a Two-Layer System , Phys. Fluids , vol. 16 , pp. 1127 – 1139 , 2004 .
   Web of Science ®Google Scholar
• P. Colinet and J. Legros , On the Hopf Bifurcation Occurring in the Two-Layer Rayleigh-Bénard Convective Instability , Phys. Fluids , vol. 6 , pp. 2631 – 2639 , 1994 .
   Web of Science ®Google Scholar
• Y. Renardy , Pattern Formation for Oscillatory Bulk-Mode Competition in a Two-Layer Bénard Problem , ZAMP , vol. 47 , no. 4 , pp. 567 – 590 , 1996 .
   Web of Science ®Google Scholar