A high-order rectilinear Lagrangian method based on the geometric conservation law
For computational fluid dynamics researchers using Lagrangian methods, this work provides a principled approach to maintain geometric conservation at high order, though it is an incremental improvement over existing techniques.
The paper develops a mesh moving strategy for high-order Lagrangian methods on quadrilateral meshes, ensuring geometric conservation and high-order accuracy. Two smooth vortex test cases confirm the scheme's feasibility.
This paper presents a mesh moving strategy for high-order Lagrangian method on quadrilateral meshes. The primary evidence of this method stems from principle of area conservative linearization and the asymptotic properties of the velocity. The former strictly adheres to the requirements of geometric conservation laws, while the latter provides a high-order accuracy guarantee. Two smooth vortex test cases verify the feasibility of the proposed scheme.