Modified nodal integral method for Navier-Stokes equations incorporated with generic quadrilateral elements, and GPU-based parallel computing

This dissertation can be broadly divided into two connected parts: development and testing of a new numerical scheme for time-dependent, incompressible Navier-Stokes (N-S) equations in non-rectangular domains; and, implementation and solution of the modified nodal integral method (MNIM), developed earlier for rectangular domains, on graphics processing units (GPUs). Nodal methods have become the backbone and workhorse of the core design production codes used in the nuclear industry for decades. As a variation of the coarse mesh nodal methods, the modified nodal integral method can accurately solve the time-dependent, incompressible N-S equations using less computation time, hence provides more efficient solution to the fluid flow problems than many other conventional schemes that rely on fine meshes. However, the transverse integration procedure (TIP) required in the formulation of the MNIM limits the scheme to be only applicable to rectangular elements. In order to remove this limitation and extend the MNIM to non-rectangular computational meshes/domains, a modified nodal integral method incorporated with generic quadrilateral elements is developed using a simple isoparametric geometry mapping. The mapping is used to transform: 1) the irregular four-node quadrilateral elements into square elements; 2) the original set of N-S equations into a set of transformed equations valid over the transformed computational domain. Then the new nodal scheme is formulated for the transformed equations. The numerical scheme developed is applied to several test problems of increasing complexity. Results show that the scheme works very well with quadrilateral elements of different shapes and degrees of distortion, maintaining the high accuracy and efficiency of the MNIM; and that the new scheme has inherent upwinding. To further enhance the computational capabilities, one needs to exploit the latest developments in computing hardware. Realizing that graphics processing units can provide superior computational power over conventional CPUs, the cutting-edge GPU-computing and the highly efficient nodal scheme are married in a double precision GPU implementation of the MNIM for the 3D, incompressible N-S equations in the second part of this dissertation. The GPU implementation is applied to simulate the lid-driven cavity flows in a unit cube and a prism with aspect ratio of two, and is validated. A performance analysis indicates that the MNIM on GPU can be an order of magnitude faster than on a CPU.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Nuclear Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Huang, Kai

Contributors dc:contributor

• Uddin, Rizwan
• Axford, Roy A.
• Jones, Barclay G.
• Pantano-Rubino, Carlos A.

• Navier-Stokes
• Nodal integral method
• Isoparametric mapping
• graphics processing units (GPU)
• Parallel computing

Statement dc:rights

• Copyright 2011 Kai Huang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/26417

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/26417