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A High-Order Discontinuous Galerkin Solver for Helically Symmetric Flows

Communications in Computational Physics 2021年第6期30卷 288-320页

作者： dominik dierkes Florian Kummer dominik Plumacher Department of Mechanical Engineering Technische Universitat DarmstadtOtto-Berndt-Straße 264287 DarmstadtGermany

We present a high-order discontinuous Galerkin(DG)scheme to solve the system of helically symmetric Navier-Stokes equations which are discussed in[28].In particular,we discretize the helically reduced Navier-Stokes equations emerging from a reduction of the independent variables such that the remaining variables are:t,r,ξwithξ=az+bϕ,where r,ϕ,z are common cylindrical coordinates and t the *** this,all three velocity components are kept non-zero.A new non-singular coordinateηis introduced which ensures that a mapping of helical solutions into the three-dimensional space is well *** that,periodicity conditions for the helical frame aswell as uniqueness conditions at the centerline axis r=0 are *** the sector near the axis of the computational domain a change of the polynomial basis is implemented such that all physical quantities are uniquely defined at the *** the temporal integration,we present a semi-explicit scheme of third order where the full spatial operator is splitted into a Stokes operator which is discretized implicitly and an operator for the nonlinear terms which is treated *** are conducted for a cylindrical shell,excluding the centerline axis,and for the full cylindrical domain,where the centerline is *** all cases we obtain the convergence rates of order O(hk+1)that are expected from DG *** addition to the first DG discretization of the system of helically invariant Navier-Stokes equations,the treatment of the central axis,the resulting reduction of the DG space,and the simultaneous use of a semi-explicit time stepper are of particular novelty.

关键词： Discontinuous Galerkin(DG) helical flows

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