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Modelling of Shallow Water Equations by Using Implicit Higher-Order<br />

Compact Scheme with Application to Dam-Break Problem<br />

Amirah Binti Azharuddin<br />

Supervisor: Dr. Ilyani Binti Abdullah<br />

Bachelor of Science (Computational Mathematics)<br />

School of Informatics and Applied Mathematics<br />

This study discusses the method of solving the non-linear shallow water equation of two<br />

dimensional space in the form of conservation with numerical simulation of dam-break<br />

problem. The scheme involved in this numerical method is a higher order compact<br />

scheme for inviscid and incompressible flow. Higher order compact scheme produces<br />

precision and strong features in the solution of finite difference methods. Additionally,<br />

these schemes use small stencils to calculate errors from governing equation and produce<br />

better solution. To solve the algebraic system, the method used is Bi-CGSTAB (Bi-<br />

Conjugate Gradient Stabilized) with preconditioning. The resulting model is a good<br />

alternative to solve the shallow water equation by replacing the existing method of the<br />

Mac-Cormack explicit method or Beam and Warming method.<br />

916 | UMT UNDERGRADUATE RESEARCH DAY 2018

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