HAMSTR - A Hybrid Unstructured-Structured Methodology



Fig. 1: Schematic representation of quadrilateral subdivision and formation of Hamiltonian loops on an unstructured triangular grid

Current computational fluid dynamics (CFD) solvers utilize either structured or unstructured grids to mesh the physical domain of interest. Unstructured grid techniques enable the discretization of complex geometries into the elementary cells with minimal effort, and allows for relatively easy implementation of adaptive mesh techniques. However, traditional unstructured grid solvers are limited in their convergence and accuracy of the solution (typically second-order) primarily because of the difficulty in finding line-structures in a purely unstructured grid. As a consequence, unstructured solvers incur a higher computational cost (3 to 10 times slower than their structured counterparts) while limiting the accuracy of the solutions obtained.

In this work, a technique was introduced to identify Hamiltonian paths on a purely unstructured grid and is applied to a unstructured surface triangular mesh, which is achieved through the quadrilateral subdivision of triangles (Fig. 1). These Hamiltonian paths are thought of as the counterpart to traditional lines on a structured mesh. To form the volume mesh, strand grids are projected from the surface nodes, which provide the structure in the wall-normal direction (Fig. 2). In totality, the formation of Hamiltonian paths and strand grids allow for high-order reconstruction schemes  and line-implcit methods on a pure unstructured mesh.


The whole process of mesh generation and the solver is written in C/C++ and is parallelized using Message Passing Interface (MPI). The general process of splitting the domain along with the scalability results are shown below in Fig 3.



Fig. 2: Process of forming the volume mesh around a fuselage starting from an unstructured mesh using Hamiltonian paths and strand grids

Fig. 3: Process of subdivision using Message Passing Interface (MPI) and the achieved speedup on both two-dimensional (airfoil) and three-dimensional (fuselage) geometries.

HAMSTR is a three-dimensional compressible viscous finite volume code. Shown in the below figures/plots are some sample solutions obtained using HAMSTR (which is based on unstructured meshes) and its comparison to available experimental data or numerical predictions from established structured solvers. The flow conditions tested range from inviscid to viscous, laminar to turbulent. 

Fig. 4: Mach contours and surface pressure distribution for Inviscid and laminar flow over a Robin fuselage.

Fig. 5: Comparison of streamlines of flow past a sphere between HAMSTR and a structured solver.


  • Govindarajan, B., Jung, Y., Baeder, J., and Sitaraman, J., “Efficient Three-Dimensional Solution for Unstructured Grids Using Hamiltonian Paths and Strand Grids,'' American Helicopter Society, Forum 71, Virginia Beach, 2015. 

  • Jung, Y. S., Govindarajan, B., and Baeder, J., “Efficient Unstructured Mesh Flow Solver Using Hamiltonian Paths and Strand Grids” The 2015 World Congress on Advances in Aeronautics, Nano, Bio, Robotics, and Energy (ANBRE15), Incheon, Korea, 25–28 August, 2015. (with a focus on turbulent flows)

  • Submitted to Journal of Computational Physics.