An adaptively refined Cartesian mesh solver for the Euler equations
Journal of Computational Physics
An accuracy assessment of Cartesian-mesh approaches for the Euler equations
Journal of Computational Physics
An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
Journal of Computational Physics
A higher-order boundary treatment for Cartesian-Grid method
Journal of Computational Physics
An upwind finite difference scheme for meshless solvers
Journal of Computational Physics
Euler calculations with embedded Cartesian grids and small-perturbation boundary conditions
Journal of Computational Physics
Implicit fully mesh-less method for compressible viscous flow calculations
Journal of Computational and Applied Mathematics
An accurate moving boundary formulation in cut-cell methods
Journal of Computational Physics
GPU computing of compressible flow problems by a meshless method with space-filling curves
Journal of Computational Physics
Hi-index | 31.47 |
The solution of the Euler equations using a "gridless" boundary condition treatment on a patched, embedded Cartesian field mesh is described. The gridless boundary treatment is implemented by means of a least squares fitting of the conserved flux variables using a cloud of nodes in the vicinity of the body. The method allows for accurate treatment of the surface boundary conditions without the need for excessive refinement of the Cartesian mesh. Additionally, the method does not suffer from problems associated with thin body geometry or extremely fine cut cells near the body. Unlike some methods that consider a gridless (or "meshless") treatment throughout the entire domain, the use of a Cartesian field mesh allows for effective implementation of multigrid acceleration, and issues associated with global conservation are alleviated. Results are presented for transonic flow about single and dual NACA 0012 airfoil configurations including a convergence study indicating the effectiveness of multigrid acceleration within the construct of the gridless boundary treatment. Where applicable, comparisons to the FLO52 body-fitted Euler code are presented to gauge the accuracy of the method.