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You searched for +publisher:"University of South Carolina" +contributor:("Zhu Wang"). Showing records 1 – 2 of 2 total matches.

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University of South Carolina

1. Yuan, Shuai. An Ensemble-Based Projection Method and Its Numerical Investigation.

Degree: PhD, Mathematics, 2020, University of South Carolina

In many cases, partial differential equation (PDE) models involve a set of parameters whose values may vary over a wide range in application problems, such as optimization, control and uncertainty quantification. Performing multiple numerical simulations in large-scale settings often leads to tremendous demands on computational resources. Thus, the ensemble method has been developed for accelerating a sequence of numerical simulations. In this work we first consider numerical solutions of Navier-Stokes equations under different conditions and introduce the ensemblebased projection method to reduce the computational cost. In particular, we incorporate a sparse grad-div stabilization into the method as a nonzero penalty term in discretization that does not strongly enforce mass conservation, and derive the long time stability and the error estimate. Numerical tests are presented to illustrate the theoretical results. A simple way to solve the linear system generated in the ensemble method is to use a direct solver. Compared with individual simulations of the same problems, the ensemble method is more efficient because there is only one linear system needs to solve for the ensemble. However, for large-scale problems, iterative linear solvers have to be used. Therefore, in the second part of this work we investigate numerical performance of the ensemble method with block iterative solvers for two typical evolution problems: the heat equation and the Navier-Stokes equations. Numerical results are provided to demonstrate the effectiveness and efficiency of the ensemble method when working together with the block iterative solvers. Advisors/Committee Members: Zhu Wang, Lili Ju.

Subjects/Keywords: Mathematics; partial differential equation; numerical simulations; Navier-Stokes equations; Navier-Stokes

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APA (6th Edition):

Yuan, S. (2020). An Ensemble-Based Projection Method and Its Numerical Investigation. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/5777

Chicago Manual of Style (16th Edition):

Yuan, Shuai. “An Ensemble-Based Projection Method and Its Numerical Investigation.” 2020. Doctoral Dissertation, University of South Carolina. Accessed April 13, 2021. https://scholarcommons.sc.edu/etd/5777.

MLA Handbook (7th Edition):

Yuan, Shuai. “An Ensemble-Based Projection Method and Its Numerical Investigation.” 2020. Web. 13 Apr 2021.

Vancouver:

Yuan S. An Ensemble-Based Projection Method and Its Numerical Investigation. [Internet] [Doctoral dissertation]. University of South Carolina; 2020. [cited 2021 Apr 13]. Available from: https://scholarcommons.sc.edu/etd/5777.

Council of Science Editors:

Yuan S. An Ensemble-Based Projection Method and Its Numerical Investigation. [Doctoral Dissertation]. University of South Carolina; 2020. Available from: https://scholarcommons.sc.edu/etd/5777


University of South Carolina

2. Zhang, Chenfei. Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State.

Degree: PhD, Mathematics, 2019, University of South Carolina

Many problems in the fields of science and engineering, particularly in materials science and fluid dynamic, involve flows with multiple phases and components. From mathematical modeling point of view, it is a challenge to perform numerical simulations of multiphase flows and study interfaces between phases, due to the topological changes, inherent nonlinearities and complexities of dealing with moving interfaces. In this work, we investigate numerical solutions of a diffuse interface model with Peng-Robinson equation of state. Based on the invariant energy quadratization approach, we develop first and second order time stepping schemes to solve the liquid-gas diffuse interface problems for both pure substances and their mixtures. The resulting temporal semi-discretizations from both schemes lead to linear systems that are symmetric and positive definite at each time step, therefore they can be numerically solved by many efficient linear solvers. The unconditional energy stabilities in the discrete sense are rigorously proven, and various numerical simulations in two and three dimensional spaces are presented to validate the accuracies and stabilities of the proposed linear schemes. Advisors/Committee Members: Lili Ju, Zhu Wang.

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; numerical solutions; two-phase diffuse interface model; Peng-Robinson equation of state; unconditional energy stabilities; invariant energy quadratization approach; temporal semi-discretizations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Zhang, C. (2019). Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/5445

Chicago Manual of Style (16th Edition):

Zhang, Chenfei. “Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State.” 2019. Doctoral Dissertation, University of South Carolina. Accessed April 13, 2021. https://scholarcommons.sc.edu/etd/5445.

MLA Handbook (7th Edition):

Zhang, Chenfei. “Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State.” 2019. Web. 13 Apr 2021.

Vancouver:

Zhang C. Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State. [Internet] [Doctoral dissertation]. University of South Carolina; 2019. [cited 2021 Apr 13]. Available from: https://scholarcommons.sc.edu/etd/5445.

Council of Science Editors:

Zhang C. Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State. [Doctoral Dissertation]. University of South Carolina; 2019. Available from: https://scholarcommons.sc.edu/etd/5445

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