Detonation Simulations with a Fifth-Order TENO Scheme

Abstract

In [Fu et al., JCP 305(2016): 333-359], a family of high-order targeted ENO (TENO) schemes is proposed. The weighting strategy of TENO either applies a candidate stencil with its optimal weight, or removes its contribution completely when it is crossed by discontinuities. This ENO-like stencil selection procedure significantly diminishes the numerical dissipation induced by the nonlinear adaptations of classical WENO schemes. In this paper, the fifth-order TENO scheme is extended to simulate reactive flows in combination with an uncoupled method [1, 2], which splits the reaction source term of detailed chemistry from the flow equations. A set of benchmark cases including the two-dimensional self-sustained detonation is simulated to validate and compare the performance of the fifth-order WENO and TENO schemes. Numerical experiments demonstrate that TENO scheme is robust for simulating chemical reacting flows with using the uncoupled method. In particular, TENO scheme shows better performance in capturing both the shockwaves and the small-scale flow structures, e.g. shear layers and vortices.

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

“…The role of transversal concentration gradient in detonation propagation was studied in Han, Wang and Law (2019c). Detonation simulations were performed in Dong et al (2019). A parallel chemistry acceleration algorithm applied to gaseous detonation was developed in Wu, Dong and Li (2019b).…”

Arbitrary high‐order extended essentially non‐oscillatory schemes for hyperbolic conservation laws

“…6,7 Numerous numerical results suggest that the smoothness-measurement methods 3,6 are essential for improving the overall performance of ENO-type schemes. [6][7][8][9][10] Moreover, the shock-detection procedure is essential for hybrid high-order finite-difference schemes. [11][12][13] In fact, the idea of hybrid schemes is straightforward and effective.…”

A multi-resolution weighted compact nonlinear scheme for hyperbolic conservation laws

“…Second-order accurate schemes are no doubt the dominating tools for most industrial computational fluid dynamics (CFD) applications Wang et al (2013). High-order schemes (third order accurate or higher), however, have received considerable attention in the CFD research community over the past decades, not only because they can effectively reduce numerically-induced dissipation and dispersion errors compared with low-order schemes Lele (1992), but yield highresolution properties which are essential for the simulation of complex flow problems Johnsen et al (2010); Ritos et al (2018); Dong et al (2019).…”