Implicit-explicit Runge-kutta Method for Combustion Simulation
نویسندگان
چکیده
New high order implicit-explicit Runge-Kutta methods have been developed and implemented into a finite volume code to solve the Navier-Stokes equations for reacting gas mixtures. The resulting nonlinear systems in each stage are solved by Newton’s method. If only the chemistry is treated implicitly, the linear systems in each Newton iteration are simple and solved directly. If in addition certain convection or diffusion terms are treated implicitly as well, the sparse linear systems in each Newton iteration are solved by preconditioned GMRES. Numerical simulations of deflagration-to-detonation transition (DDT) show the potential of the new time integration for computaional combustion.
منابع مشابه
New Hybrid Runge–Kutta Methods for Unsteady Reactive Flow Simulation
In the numerical simulation of transient reacting flow, standard explicit calculation is prohibitively expensive because of the small time steps needed to address the stiffness of a governing differential system. To circumvent this, new hybrid implicit–explicit methods proposed treat the stiffness, whereas the underlying time-step control is governed by the Courant stability criterion. Because ...
متن کاملHigh-Order Implicit Time Integration for Unsteady Compressible Fluid Flow Simulation
This paper presents an overview of high-order implicit time integration methods and their associated properties with a specific focus on their application to computational fluid dynamics. A framework is constructed for the development and optimization of general implicit time integration methods, specifically including linear multistep, Runge-Kutta, and multistep Runge-Kutta methods. The analys...
متن کاملLow-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional ODE systems
Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storag...
متن کاملGPU Implementation of Implicit Runge-Kutta Methods
Runge-Kutta methods are an important family of implicit and explicit iterative methods used for the approximation of solutions of ordinary differential equations. Explicit RungeKutta methods are unsuitable for the solution of stiff equations as their region of stability is small. Stiff equation is a differential equation for which certain numerical methods for solving the equation are numerical...
متن کاملAdditive Semi-Implicit Runge-Kutta Methods for Computing High-Speed Nonequilibrium Reactive Flows
This paper is concerned with time-stepping numerical methods for computing sti semi-discrete systems of ordinary di erential equations for transient hypersonic ows with thermo-chemical nonequilibrium. The sti ness of the equations is mainly caused by the viscous ux terms across the boundary layers and by the source terms modeling nite-rate thermo-chemical processes. Implicit methods are needed ...
متن کامل