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Steady-State Low-Order Explicit (LOE) Runge-Kutta Schemes with Improved Convergence

Sabri, Zaid
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1588722753648659

Abstract Details

2020, Master of Science, University of Toledo, Mechanical Engineering.
In Computational Fluid Dynamics, numerical schemes are used to integrate the time derivative to march a solution in time. One common time integration technique is the explicit Runge-Kutta scheme, which is used to obtain high orders of accuracy through a multistage procedure. Researchers have used and optimized high number of stages to obtain both high accuracy and inviscid stability limits. Recent research has shown that higher-order Runge-Kutta schemes' accuracy is degrading near the boundaries. Hence, a time marching scheme with low number of stages is desired. In this work, low order explicit (LOE) Runge-Kutta schemes are optimized to achieve high inviscid stability limits. Single-step and multi-step schemes are compared to higher-order schemes. The resulting schemes obtain nearly 90% of the stability limit per stage of the optimized Jameson five-stage scheme while using 50% fewer stages per time step, and over 80% of the stability limit per stage of the Allampalli HALE-RK67 scheme while using 60% fewer stages per time step.
Ray Hixon (Committee Chair)
Sorin Cioc (Committee Member)
Chunhua Sheng (Committee Member)
107 p.
Aerospace Materials; Fluid Dynamics; Mechanical Engineering
Runge-Kutta; Euler Equation; CFD; CAA; Stability; Numerical Schemes; Alternating Runge-Kutta Schemes; Time Marching; Explicit Time Marching

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Citations

  • Sabri, Z. (2020). Steady-State Low-Order Explicit (LOE) Runge-Kutta Schemes with Improved Convergence [Master's thesis, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1588722753648659

    APA Style (7th edition)

  • Sabri, Zaid. Steady-State Low-Order Explicit (LOE) Runge-Kutta Schemes with Improved Convergence. 2020. University of Toledo, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1588722753648659.

    MLA Style (8th edition)

  • Sabri, Zaid. "Steady-State Low-Order Explicit (LOE) Runge-Kutta Schemes with Improved Convergence." Master's thesis, University of Toledo, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1588722753648659

    Chicago Manual of Style (17th edition)

toledo1588722753648659
141
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This open access ETD is published by University of Toledo and OhioLINK.