Séminaire LMFA (présentiel - École Centrale) : Fluid-acoustic coupling analysis by discrete differential forms

Présenté par : Hiroki Fukagawa
Representative Director, DeepFlow, Inc

Lien vers la page d'annonce du LMFA

We developed a super-large-scale, high-accurate, and high-speed physical field simulator, Elkurage, that uses discrete differential forms and conducted a direct numerical simulation of fluid-acoustic interactions that solves the Navier-Stokes equations for compressible fluids. It helps reduce the noise of a wind turbine, an air-conditioner, and a high-speed rail train.

Physical fields described in differential forms can be discretized into discrete differential forms by an evaluation that naturally transforms the locality and parallelism of physical phenomena into the ones of data access. This method uses a staggered unstructured grid consisting of primal cells and dual cells. The cells are defined hierarchically as 3-cells, 2-cells, 1-cells, and 0-cells, representing volume, area, length, and vertexes. In this layout, mass density and velocity field are discretized as the total mass in primal 3-cells and the total mass flux in primal 2-form.

An explicit method for the equations given in differential forms with this arrangement minimizes computational errors related to mass or pressure as the finite-difference methods (FDM) for partial differential equations with the staggered grid where the calculation points are arranged along with coordinate systems.

Incorporating simulations into the design process requires importing complex CAD design data. FDM is unsuitable for complex surface geometries because a surface that does not follow the coordinate system is expressed as a staircase. On the other hand, our method uses various elements and has an advantage in the shape expression for industrial design compared to FDM.