Forward, tangent linear, and adjoint Runge–Kutta methods for stiff chemical kinetic simulations

Abstract

This paper investigates numerical methods for direct decoupled sensitivity and discrete adjoint sensitivity analysis of stiff systems based on implicit Runge–Kutta schemes. Efficient implementations of tangent linear and adjoint schemes are discussed for two families of methods: fully implicit three-stage Runge–Kutta and singly diagonally-implicit Runge–Kutta. High computational efficiency is attained by exploiting the sparsity patterns of the Jacobian and Hessian. Numerical experiments with a large chemical system used in atmospheric chemistry illustrate the power of the stiff Runge–Kutta integrators and their tangent linear and discrete adjoint models. Through the integration with the Kinetic PreProcessor KPP–2.2 these numerical techniques become readily available to a wide community interested in the simulation of chemical kinetic systems.