Application of Diagonally Implicit Runge-Kutta Method for Solving Time-Dependent Convection-Diffusion Equation

Deng Zhihong; Sun Yuliang; Li Fu; Rizwan-uddin

Feb. 2025

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Deng Zhihong, Sun Yuliang, Li Fu, Rizwan-uddin. Application of Diagonally Implicit Runge-Kutta Method for Solving Time-Dependent Convection-Diffusion Equation[J]. Nuclear Power Engineering, 2014, 35(1): 5-9.

Citation:

Deng Zhihong, Sun Yuliang, Li Fu, Rizwan-uddin. Application of Diagonally Implicit Runge-Kutta Method for Solving Time-Dependent Convection-Diffusion Equation[J]. Nuclear Power Engineering, 2014, 35(1): 5-9.

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Application of Diagonally Implicit Runge-Kutta Method for Solving Time-Dependent Convection-Diffusion Equation

1. Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing, 100084, China;
2. China Huaneng Nuclear Development Co. Ltd. Beijing, 100036, China;
3. Nuclear, Plasma, Radiological Engineering, University of Illinois at Urbana-Champaign, Urbana, 61801, USA

Received Date: 2012-10-08
Rev Recd Date: 2013-10-22

Available Online: 2025-02-15

Abstract

Abstract

An efficient scheme for solving transient convection-diffusion equation was developed. Modified nodal expansion method（MNEM） was utilized for spatial discretization, while two kinds of diagonally implicit Runge-Kutta（DIRK） schemes—second-order DIRK and fourth-order DIRK were adopted for time discretization. The numerical results show that the numerical results of TDMNEM code agree with analytical solutions very well. MNEM has good ability in capturing sharp temperature variation. The efficiency of two time discretization methods depend on problem and the error criteria which been selected.
- Modified nodal expansion method,
- Convection-diffusion equation,
- Diagonally implicit Runge-Kutta schemes