A component-splitting implicit time integration for multicomponent reacting flows simulations

TL;DR

The paper tackles the challenge of slow convergence and high cost in implicit time integration for thermochemical nonequilibrium, multicomponent flows by introducing a component-splitting approach that independently solves flow and species equations with distinct spectral-radii-based flux splitting. The implicit operator is split into a flow block and a component block, and consistence corrections are applied to maintain mass conservation and fraction consistency as iterations proceed. Numerical tests across cylinders, ASWBLI, a GSC capsule, and a winged missile demonstrate that component-splitting reduces both iteration counts and per-iteration time, yields lower residuals, and improves wall-heat-flux accuracy, with acceleration growing with CFL and species count. The method shows strong robustness and accuracy, suggesting practical impact for efficient simulation of high-speed, chemically reacting flows and potential coupling with sparse chemistry techniques for even greater gains.$

Abstract

A component-splitting method is proposed to improve convergence characteristics for implicit time integration of compressible multicomponent reactive flows. The characteristic decomposition of flux jacobian of multicomponent Navier-Stokes equations yields a large sparse eigensystem, presenting challenges of slow convergence and high computational costs for implicit methods. To addresses this issue, the component-splitting method segregates the implicit operator into two parts: one for the flow equations (density/momentum/energy) and the other for the component equations. Each part's implicit operator employs flux-vector splitting based on their respective spectral radii to achieve accelerated convergence. This approach improves the computational efficiency of implicit iteration, mitigating the quadratic increase in time cost with the number of species. Two consistence corrections are developed to reduce the introduced component-splitting error and ensure the numerical consistency of mass fraction. Importantly, the impact of component-splitting method on accuracy is minimal as the residual approaches convergence. The accuracy, efficiency, and robustness of component-splitting method are thoroughly investigated and compared with the coupled implicit scheme through several numerical cases involving thermo-chemical nonequilibrium hypersonic flows. The results demonstrate that the component-splitting method decreases the required number of iteration steps for convergence of residual and wall heat flux, decreases the computation time per iteration step, and diminishes the residual to lower magnitude. The acceleration efficiency is enhanced with increases in CFL number and number of species.

Figures (13)

• Figure 1: Growth ratio on the CPU time and speed-up ratio with respect to the growth ratio on the number of species from $ns=16$ to $ns=4096$.
• Figure 2: Computational grid of cylinder with radius of 45 mm:(a)cylinder2D; (b)cylinder3D.
• Figure 3: Convergence curve of residual and heat flux with respect to iteration step for comparison of the CS and CI method in the cylinder case: ((a)(d)) residual of specie density; ((b)(e)) residual of energy; ((c)(f)) wall heat flux at stagnation points and CPU time cost; ((a)(b)(c)) cylinder2D; ((d)(e)(f)) cylinder3D. The dashed lines represent convergence criteria.
• Figure 4: Comparison of wall pressure and heat flux between CS, CI, and experimental data KNIGHT20128 for hypersonic flows on cylinder.(a):cylinder2D;(b)cylinder3D
• Figure 5: Convergence curve of the residual:((a),(c))$L_2$ norm of sum of residual of specie density and CPU time; ((b),(d))$L_2$ norm of sum of residual of energy and wall heat flux at stagnation points;((a),(b))$ns=11$ case;((c),(d))$ns=5$ case.