## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2013 (2013), Article ID 920912, 12 pages.

### Numerical Study of Violent Impact Flow Using a CIP-Based Model

Qiao-ling Ji, Xi-zeng Zhao, and Sheng Dong

#### Abstract

A two-phase flow model is developed to study violent impact flow problem. The model governed by the Navier-Stokes equations with free surface boundary conditions is solved by a Constrained Interpolation Profile (CIP)-based high-order finite difference method on a fixed Cartesian grid system. The free surface is immersed in the computation domain and expressed by a one-fluid density function. An accurate Volume of Fluid (VOF)-type scheme, the Tangent of Hyperbola for Interface Capturing (THINC), is combined for the free surface treatment. Results of another two free surface capturing methods, the original VOF and CIP, are also presented for comparison. The validity and utility of the numerical model are demonstrated by applying it to two dam-break problems: a small-scale two-dimensional (2D) and three-dimensional (3D) full scale simulations and a large-scale 2D simulation. Main attention is paid to the water elevations and impact pressure, and the numerical results show relatively good agreement with available experimental measurements. It is shown that the present numerical model can give a satisfactory prediction for violent impact flow.

#### Article information

**Source**

J. Appl. Math., Volume 2013 (2013), Article ID 920912, 12 pages.

**Dates**

First available in Project Euclid: 14 March 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1394808156

**Digital Object Identifier**

doi:10.1155/2013/920912

#### Citation

Ji, Qiao-ling; Zhao, Xi-zeng; Dong, Sheng. Numerical Study of Violent Impact Flow Using a CIP-Based Model. J. Appl. Math. 2013 (2013), Article ID 920912, 12 pages. doi:10.1155/2013/920912. https://projecteuclid.org/euclid.jam/1394808156