A Frequency Domain Solver



As a companion to the time-domain HDPhysics-T, HyPerComp has also developed a high order frequency domain code called HDPhysics-F, which is also based on the DG approach. One approach that exhibits both high accuracy and nearly perfect scaling with the number of processors is the Ultra Weak Variational Formulation that has been implemented in 3D by Monk and Huttunen. HDPhysics-F and HDPhysics-T share similar attributes, however HDPhysics-F can go to a much higher order in plane wave basis functions and can employ much larger cell sizes compared to HDPhysics-T.



FEATURES





Each element in 3D grid is its own universe: Both, its shape and the basis functions used inside the element can be varied independent of the choices made for its neighbors



  • Current UWVF implementation uses plane wave (PW) basis function
  • Spherical and polynomial basis in progress
    • Arbitrary cell shapes (tet, hex, prism, pyramid and any polyhedral shape)


High order mathematical framework



  • Chooses the order P of PW set inside a cell based on the cell size in wavelengths
  • Current implementation allows P to reach 1200 to 10 λ cell sizes


Formulation allows for high order curved meshing



  • Elasticity approach for creation of curved meshing


Solves for tangential fields at cell interfaces - volumetric DG-based operation



  • Inter-processor communication only at nodal boundaries
  • Scalable on fine grain parallel clusters
  • Computationally efficient and well suited for large-scale simulations


APPLICATIONS





Small, Medium, Large and Very Large Cavity Test Cases



1.25λ x 1.25λ x 1.875λ Small Size Cavity



Computational Efficiency from High Order Methods and Large Cells



24λ x 24λ x 200λ Square Cavity



10λ Cell Size Provides Computational Efficiency to Modeling a Trihedron



Modeling Large Inlets Using Curved Meshing



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