A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

• A high-order finite-volume method is developed for mapped grids.
• The algorithm is highly parallel and features adaptive mesh refinement.
• The numerical algorithm is freestream-preserving.
• The algorithm is verified to be fourth-order accurate and conservative.
• The algorithm solves unsteady shock problems with strong discontinuities.

A fourth-order accurate finite-volume method is presented for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. These considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge–Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution of a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.