Numerical Treatment of Parametric Gradient Problems in Source Term by New Difference Methods

CSME 2018/12
Volume 39 No.6 : 609-618

Numerical Treatment of Parametric Gradient Problems in Source Term by New Difference Methods

Tzong-Hann Shieh^a, Meng-Rong Li^b, Yu-Tso Li^c and Yung-Ting Chen
^aDepartment of Aerospace and Systems Engineering, Feng Chia University. 100, Wenhwa Rd., Seatwen, Taichung, Taiwan. / Ph.D. Program of Mechanical and Aeronautical Engineering, Feng Chia University. 100, Wenhwa Rd., Seatwen, Taichung, Taiwan.
^bDepartment of Mathematical Sciences, National Chengchi University. 64, Sec. 2, ZhiNan Rd., Wenshan District, Taipei, Taiwan.
^cPh.D. Program of Mechanical and Aeronautical Engineering, Feng Chia University. 100, Wenhwa Rd., Seatwen, Taichung, Taiwan. / Department of Mechanical Engineering, Minghsin University of Science and Technology. No.1, Xinxing Rd., Xinfeng Hsinchu 30401, Taiwan

Abstract: In this paper, we expand the energy equation of unsteady Euler equations as the form of mixture gas and carry out the numerical resolution through the FVM to discuss the nonphysical oscillations near the contact discontinuity interface and shock wave. We resolve the equations by using the AUSMDV Riemann solver with different flux limiters, the FVM and the second-order with two-step discrete-time stepping method. For the source term in the investigated Euler equations with multi-species, we discuss the facing problem of for the numerical treatment of gradient in different type and test the non-physical oscillation problem by establishing a new applied method of gradient control.

Keywords: gradient method, Euler equations, numerical oscillation, shock capturing.

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