Simulation of viscous water column collapse using adapting hierarchical grids

An adaptive hierarchical grid based method for predicting complex free surface flows is used to simulate collapse of a water column. Adapting quadtree grids are combined with a high-resolution interface capturing approach and pressure based coupling of the Navier Stokes equations. The Navier-Stokes flow solution scheme is verified for simulation of flow in a lid driven cavity at Re=1000. Two approaches to the coupling of the Navier-Stokes equations are investigated as are alternative face velocity and hanging node interpolations. Collapse of a water column as well as collapse of a water column and its subsequent interaction with an obstacle are simulated. The calculations are made on uniform and adapting quadtree grids, and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. Results are in excellent agreement with experimental and other numerical data. A sharp interface is maintained at the free surface. The new adapting quadtree-based method achieves a considerable saving in the size of the computational grid and CPU time in comparison with calculations made on equivalent uniform grids.

[1]  Dong-Yol Yang,et al.  Finite element analysis of transient fluid flow with free surface using VOF (volume-of-fluid) method and adaptive grid , 1998 .

[2]  Deborah Greaves,et al.  Simulation of interface and free surface flows in a viscous fluid using adapting quadtree grids , 2004 .

[3]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

[4]  O. Ubbink.  Numerical prediction of two fluid systems with sharp interfaces , 1997 .

[5]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[6]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .

[7]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[8]  Ling Qian,et al.  Cartesian Cut Cell Two-Fluid Solver for Hydraulic Flow Problems , 2003 .

[9]  Deborah Greaves,et al.  Hierarchical tree-based finite element mesh generation , 1999 .

[10]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[11]  R. Eatock Taylor,et al.  Numerical simulation of sloshing waves in a 3D tank , 1998 .

[12]  James M. Hyman,et al.  Numerical methods for tracking interfaces , 1984 .

[13]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[14]  S. Atluri,et al.  The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations , 2001 .

[15]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[16]  Hideaki Miyata,et al.  Finite-difference simulation of breaking waves , 1986 .

[17]  P. Roache.  Perspective: A Method for Uniform Reporting of Grid Refinement Studies , 1994 .

[18]  Deborah Greaves,et al.  A quadtree adaptive method for simulating fluid flows with moving interfaces , 2004 .

[19]  Derek M. Causon.  An efficient front-tracking algorithm for multi-component flow calculations with biomedical applications , 1996 .

[20]  Bertrand Alessandrini,et al.  A 2D+T VOF fully coupled formulation for the calculation of breaking free-surface flow , 2004 .

[21]  Dong-Yol Yang,et al.  Three-dimensional finite element analysis of transient fluid flow with free-surface using marker surface method and adaptive grid refinement , 1999 .

[22]  Deborah Greaves,et al.  On the use of adaptive hierarchical meshes for numerical simulation of separated flows , 1998 .

[23]  A. Gosman,et al.  High resolution NVD differencing scheme for arbitrarily unstructured meshes , 1999 .

[24]  Alistair G.L. Borthwick,et al.  Finite‐volume‐type VOF method on dynamically adaptive quadtree grids , 2004 .

[25]  S. Popinet.  Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries , 2003 .

[26]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[27]  C. K. Thornhill,et al.  Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane , 1952, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.