Verification and application of Riemann boundary condition on high-order unstructured finite volume methods

Riemann boundary condition is one of the boundary conditions with weak-imposition approach, which employs the finite wave model to treat boundary conditions of subsonic inlet, outlet and far field by solving the corresponding Riemann problems. Hence, such an imposition process is effectively simplified, and complex derivations based on the characteristic relation and Riemann invariants are completely avoided. By the introduction of this weak-imposition approach, a better numerical performance on second-order unstructured finite volume methods has already been achieved. In order to further verify the application value of this novel boundary condition, it is extended to high-order unstructured finite volume discretization in this study. The numerical performance of this boundary condition is verified in the flow with manufactured solutions (MMS) and real subsonic flows including the inviscid circular flow and the unsteady flow with initial gauss pulse disturbances. Based on computational results, the designed order of accuracy is not deteriorated by the employment of the Riemann boundary condition, and characteristics at the outlet is well reflected compared to the commonly used non-reflective boundary condition based on one-dimensional Riemann invariants. This novel boundary condition is simpler to impose, and provides a more efficient subsonic boundary processing method for high-order numerical simulations based on unstructured finite volume methods.