Abstract
For the numerical simulation of convection-dominated reacting flow problems governed by convection-reaction equations, grids-based Eulerian methods may cause different degrees of either numerical dissipation or unphysical oscillations. In this paper, a Lagrangian particle algorithm based on the smoothed particle hydrodynamics (SPH) method is proposed for convection-reaction equations and is applied to an autocatalytic reaction model with multicomponent reactants. Four typical Eulerian methods are also presented for comparison, including the high-resolution technique with the Superbee flux limiter, which has been considered to be the most appropriate technique for solving convection-reaction equations. Numerical results demonstrated that when comparing with traditional first- and second-order schemes and the high-resolution technique, the present Lagrangian particle algorithm has better numerical accuracy. It can correctly track the moving steep fronts without suffering from numerical diffusion and spurious oscillations.
Highlights
The objective of this paper is to develop a Lagrangian particle algorithm based on a smoothed particle hydrodynamics (SPH) method for convection-reaction equations to enhance both the numerical accuracy and computational efficiency
It is seen that with an increased grid number the upstream difference scheme (UDS) results converge to a particular solution, which is similar to the conclusion that the limitation of UDS for solving convection-diffusion equation converges to the theoretical solution [3]
Since there is no exact solution for the autocatalytic reaction model considered the UDS solution with grid number
Summary
Reacting flow models play an important role in the simulation of many physical and engineering problems, such as the pollutant transport process in water and air, heat conduction process in flowing fluids, chromatography column in reactors [1], and high-speed eddy current in electromagnetic fields [2]. Alhuamaizi [7] concluded that high-resolution techniques such as FCT, MUSCL and WENO schemes and TVD with flux limiters, are all efficient for tracking steep moving fronts and are essential for cases which use small numbers of grid points. In terms of both accuracy and computing time, the Superbee flux limiter is found to be the most appropriate method for simulating the sharp fronts of the reactor model. The objective of this paper is to develop a Lagrangian particle algorithm based on a smoothed particle hydrodynamics (SPH) method for convection-reaction equations to enhance both the numerical accuracy and computational efficiency.
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