Continuous adjoint based error estimation and r-refinement for the active-flux method

摘要

This paper explores the possibility of using continuous adjoints to estimate errors in scalar outputs and to drive mesh adaptation for the active-flux method. Compared to a discrete adjoint approach, the continuous adjoint offers a few attractive advantages for the active-flux method, such as a naturally fully-discrete, explicit implementation that parallels the simplicity of the primal system evolution and error estimates obtained from integrals over the space-time control volumes. The latter point is important because the active flux method does not possess a variational formulation. In addition, we present novel unsteady adaptation mechanics that rely on dynamically moving mesh nodes, i.e. r-reflnement, in order to minimize the output error.