Hope: A High-Order 3D Panel Method
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Low-fidelity methods based on potential flow theory such as the Vortex or Doublet Lattice Methods (VLM, DLM) are still widely applied in engineering applications, where the computational cost of high-fidelity CFD is prohibitive, e.g., for mass simulations in the load analysis process for aircraft design. For many of these applications, panel methods represent an increase in fidelity, since they capture relevant three-dimensional effects related to thickness and surface geometry which DLM and VLM omit. This talk introduces Hope, a three-dimensional panel method based on the Morino formulation applying Dirichlet boundary conditions. Traditional low-order panel methods are usually restricted to element-wise constant potentials including doublet jumps at the panel boundaries, which induce spurious vortex velocities. While these merely affect the local boundary condition fulfillment for subsonic flows, they may prevent the correct solution of supersonic cases. In contrast, the implementation presented here enforces the boundary conditions in a weighted residual sense with a Galerkin-type formulation. This enables the representation of potentials with higher-order basis functions, which do not only offer improved convergence rates but are also continuous at element boundaries. Furthermore, they allow for the strictly element-local evaluation of surface velocities, avoiding the need for specialized finite-difference schemes and, thus, improving numerical robustness. The implementation is designed as a modern C++ library with a Python interface, combining computational performance of the former with accessibility of the latter. Special emphasis was given to software design targeting ease of use, extensibility and maintainability. The Python interface in particular enables straight-forward coupling to other solvers or integration into existing frameworks. Representative results are presented and compared to established reference data in order to illustrate the capabilities and accuracy of this solver.
