In this paper, we provide an overview of the soon-to-be released program meshCurve. The software aims to be a user-friendly tool to convert linear unstructured meshes to curved high-order meshes, based on a geometry reconstruction procedure. Usability and accuracy are its goals. Using state-of-the-art algorithms, the software reconstructs a highorder curved surface from the linear surface mesh, while retaining sharp feature edges from the original low-order surface. The upgrade process is automatic and does not require a CAD file. meshCurve may be used by CFD practitioners and researchers to easily produce quality high-order meshes from existing low-order meshes. The CGNS standard is used as the file format for input and output.

and the Graduate Faculty of the University of Kansas in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

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The conventional CFD solvers depend on a mesh to discretize the domain. Due to the flexible nature of meshless methods, which do not require a mesh, we re-examine several meshless solvers for possible applications to moving boundary problems. Like many meshdependent solvers, second order meshless solvers suffer from convergence problems for transonic and supersonic flows with shock waves. In this work we develop a convergent limiter following ideas for finite volume solvers. The meshless solver is tested with a supersonic flow in a channel and subsonic flow over an airfoil and rigid body, and machine zero convergence is achieved for both the testing cases. We plan to run more benchmark problems, and further extend the present meshless solver to handle moving boundary problems. Nomenclaturec = shape parameter Cp = pressure coefficient dt = time step f, g = generic functions F1 = Flux vector in x-direction F2 = Flux vector in y-direction G = Flux vector along a given direction i = index of reference node j = index of supporting node k = index of neighboring nodes NI = number of supporting nodes n = time index during navigation Q = Vector of conservative variables r = distance between two nodes T = temperature x = position vector = limiter = radial basis function M  = Mach number of the free stream

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