1  Introduction

This document is automatically generated from the results obtained when running the Gerris test suite. The test suite is run daily on the development branch of the version-controlled source code.

Note that the stable branch (from which snapshot versions and packages are generated) is only updated when all of the tests succeed i.e. the status of the test cases below reflects the state of the development branch only.

2  Poisson

• PASS: Convergence of the Poisson solver
  • PASS: Convergence with a refined circle
  • PASS: Dirichlet boundary condition
• PASS: Convergence of the Poisson solver with solid boundaries
  • PASS: Star-shaped solid boundary
  • PASS: Star-shaped solid boundary with refinement
  • PASS: Thin wall at box boundary
• PASS: Poisson solution in a dumbbell-shaped domain

3  Advection and diffusion

• PASS: Convergence of the Godunov advection scheme
• PASS: Time-reversed VOF advection in a shear flow
  • PASS: Time-reversed advection with curvature-based refinement
• PASS: Comparison between the explicit and implicit diffusion schemes
• PASS: Conservation of diffusive tracer

4  Euler

• PASS: Estimation of the numerical viscosity
  • PASS: Estimation of the numerical viscosity with refined box
• PASS: Convergence for a simple periodic problem
• PASS: Convergence for the three-way vortex merging problem
• PASS: Flow created by a cylindrical volume source

5  Axisymmetric

• PASS: Potential flow around a sphere
  • PASS: Viscous flow past a sphere
• PASS: Mass conservation
  • PASS: Mass conservation with solid boundary

6  Navier-Stokes

• PASS: Lid-driven cavity at Re=1000
  • PASS: Lid-driven cavity at Re=1000 (explicit scheme)
  • PASS: Lid-driven cavity on an anisotropic mesh
• PASS: Poiseuille flow
  • PASS: Bagnold flow of a granular material
• PASS: Creeping Couette flow of Generalised Newtonian fluids
• PASS: Momentum conservation for large density ratios
• PASS: Hydrostatic balance with solid boundaries and viscosity
  • PASS: Hydrostatic balance with quadratic pressure profile
• PASS: Coriolis formulation in 3-D
• PASS: Wind-driven lake

7  Solid boundaries

• PASS: Convergence of a potential flow solution
• PASS: Flow through a divergent channel
• PASS: Potential flow around a thin plate

8  Moving solid boundaries

• PASS: Translation of an hexagon in a uniform flow
• PASS: Bénard–von Kármán vortex street behind a cylinder translating in a fluid at rest

9  Surface tension

• PASS: Circular droplet in equilibrium
  • PASS: Axisymmetric spherical droplet in equilibrium
• PASS: Planar capillary waves
  • PASS: Fluids of different densities
  • PASS: Air-Water capillary wave
  • PASS: Pure gravity wave
• PASS: Shape oscillation of an inviscid droplet

10  Shallow-water

• PASS: Geostrophic adjustment
  • PASS: Geostrophic adjustment on a beta-plane
• PASS: Coastally-trapped waves
  • PASS: Coastally-trapped waves with adaptive refinement
• PASS: Gravity waves in a realistic ocean basin

11  Saint-Venant

• PASS: Oscillations in a parabolic container

12  General Orthogonal Coordinates

• PASS: Circular dam break on a sphere
  • PASS: Circular dam break on a rotating sphere
• PASS: Advection of a cosine bell around the sphere
• PASS: Poisson problem with a pure spherical harmonics solution
  • PASS: Spherical harmonics with longitude-latitude coordinates
• PASS: Poisson equation on a sphere with Gaussian forcing
  • PASS: Gaussian forcing using longitude-latitude coordinates

13  Electrohydrodynamics

• PASS: Dielectric-dieletric planar balance
  • PASS: Balance with solid boundaries
• PASS: Relaxation of a charge bump
• PASS: Charge relaxation in an axisymmetric insulated conducting column
  • PASS: Charge relaxation in a planar cross-section
• PASS: Equilibrium of a droplet suspended in an electric field

References

[1]

A. S. Almgren, J. B. Bell, P. Colella, L. H. Howell, and M. L. Welcome. A conservative adaptive projection method for the variable density incompressible navier-stokes equations. J. Comput. Phys., 142:1–46, 1998.

[2]

A. S. Almgren, J. B. Bell, P. Colella, and T. Marthaler. A cartesian grid projection method for the incompressible euler equations in complex geometries. SIAM J. Sci. Comp., 18(5):1289–1309, 1997.

[3]

R. B. Bird, R. C. Armstrong, and O. Hassager. Dynamics of polymeric liquids. Wiley-Interscience, second edition edition, 1987.

[4]

A. Blanco and J. Magnaudet. The structure of the axisymmetric high-Reynolds number flow around an ellipsoidal bubble of fixed shape. Physics of Fluids, 7:1265, 1995.

[5]

J. P Boyd and C. Zhou. Three ways to solve the Poisson equation on a sphere with Gaussian forcing. Journal of Computational Physics, 228(13):4702–4713, 2010.

[6]

E. Curchitser. Waves in a circular basin. Technical report, Rutgers University, 2005.

[7]

K. K. Droegemeier. Advanced Regional Prediction System User guide (Version 4.0). Technical report, University of Oklahoma, 2007. Section 13.4.

[8]

F. Dupont. Comparison of numerical methods for modelling ocean circulation in basins with irregular coasts. PhD thesis, McGill University, Montreal, 2001.

[9]

EA Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 161(1):35–60, 2000.

[10]

B. Fornberg. Steady viscous flow past a sphere at high Reynolds number. J. Fluid Mech., 190:471, 1988.

[11]

D. Gerlach, G. Tomar, G. Biswas, and F. Durst. Comparison of surface tension methods for surface tension dominant two-phase flows. Int. J. Heat Mass Transfer, 49:740–754, 2006.

[12]

D. Gueyffier, A. Nadim, J. Li, R. Scardovelli, and S. Zaleski. Volume of fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comp. Phys., 152:423–456, 1998.

[13]

Rossmanith J. A, D. S. Bale, and R. J. LeVeque. A wave propagation algorithm for hyperbolic systems on curved manifolds. Journal of Computational Physics, 199:631–662, 2004.

[14]

H. Johansen and P. Colella. A cartesian grid embedded boundary method for Poisson equation on irregular domains. Journal of Computational Physics, 147(1):60–85, 1998.

[15]

H. Lamb. Hydrodynamics. Dover, 1932.

[16]

D. Y. Leroux and C. A. Lin. Finite elements for shallow-water equations ocean models. Monthly Weather Review, 126:1931–1951, 1998.

[17]

Q. Liang and A.G.L. Borthwick. Adaptive quadtree simulation of shallow flows with wet–dry fronts over complex topography. Computers and Fluids, 2008.

[18]

D. R. Lynch and F. E. Werner. 3-D hydrodynamics on finite elements. Part i: linearized harmonic model. Int. J. for Num. Methods in Fluids, (7):871–909, 1987.

[19]

J.H. Masliyah and N. Epstein. Numerical study of steady flow past spheroids. Journal of Fluid Mechanics, 44(03):493–512, 1970.

[20]

M. L. Minion. A projection method for locally refined grids. J. Comput. Phys., 127:158–177, 1996.

[21]

J. Peraire, O. C. Zienkiewicz, and K. Morgan. Shallow water problems: a general explicit formulation. Int. J. for Num. Methods in Eng., 22:547–574, 1986.

[22]

S. Popinet. Gerris: a tree-based adaptive solver for the incompressible euler equations in complex geometries. J. Comput. Phys., 190(2):572–600, 2003.

[23]

S. Popinet and S. Zaleski. A front tracking algorithm for the accurate representation of surface tension. Int. J. Numer. Meth. Fluids, 30:775–793, 1999.

[24]

A. Prosperetti. Motion of two superposed viscous fluids. Phys. Fluids, 24:1217–1223, 1981.

[25]

W. J. Rider. Approximate projection methods for incompressible flows: Implementation, variants and robustness. Technical Report LA-UR-2000, Los Alamos National Laboratory, 1995.

[26]

J.A. Rossmanith. A wave propagation method for hyperbolic systems on the sphere. Journal of Computational Physics, 213(2):629–658, 2006.

[27]

M. Rudman. Volume-tracking methods for interfacial flow calculations. International Journal for Numerical Methods in Fluids, 24(7):671–691, 1997.

[28]

J. Sampson, A. Easton, and M. Singh. Moving boundary shallow water flow above parabolic bottom topography. ANZIAM J, 47, 2006.

[29]

G. I. Taylor. Studies in electrohydrodynamics I. The circulation produced in a drop by an electric field. Proc. R. Soc. Lon. A, 291:159–166, 1966.

[30]

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado. Two-phase electrohydrodynamic simulations using a volume-of-fluid approach. Journal of Computational Physics, 227(2):1267–1285, 2007.

[31]

D. J. Torres and J. U. Brackbill. The point-set method: front-tracking without connectivity. J. Comput. Phys., 165:620–644, 2000.

[32]

C.T. Shin U. Ghia, K.N. Ghia. High-Re solution for incompressible flow using the Navier-Stokes equations and the multigrid method. J. Comput. Phys., 48:387–411, 1982.

[33]

D. Vola, F. Babik, and J.-C Latché. On a numerical strategy to compute gravity currents of non-newtonian fluids. J. Comput. Phys., 201(2):397–420, 2004.

[34]

D. L. Williamson, J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber. A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics, 102:211–224, 1992.

[35]

N. Zhang and Z.C. Zheng. An improved direct-forcing immersed-boundary method for finite difference applications. Journal of Computational Physics, 221:250–268, 2007.

This document was translated from L^AT_EX by H^EV^EA.