10 research outputs found
Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes II: unsteady flows
For the simulations of unsteady flow, the global time step becomes really
small with a large variation of local cell size. In this paper, an implicit
high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on
the time step for unsteady simulations. In order to improve the efficiency and
keep the high-order accuracy, a two-stage third-order implicit time-accurate
discretization is proposed. In each stage, an artificial steady solution is
obtained for the implicit system with the pseudo-time iteration. In the
iteration, the classical implicit methods are adopted to solve the nonlinear
system, including the lower-upper symmetric Gauss-Seidel (LUSGS) and
generalized minimum residual (GMRES) methods. To achieve the spatial accuracy,
the HGKSs with both non-compact and compact reconstructions are constructed.
For the non-compact scheme, the weighted essentially non-oscillatory (WENO)
reconstruction is used. For the compact one, the Hermite WENO (HWENO)
reconstruction is adopted due to the updates of both cell-averaged flow
variables and their derivatives. The expected third-order temporal accuracy is
achieved with the two-stage temporal discretization. For the smooth flow, only
a single artificial iteration is needed. For uniform meshes, the efficiency of
the current implicit method improves significantly in comparison with the
explicit one. For the flow with discontinuities, compared with the well-known
Crank-Nicholson method, the spurious oscillations in the current schemes are
well suppressed. The increase of the artificial iteration steps introduces
extra reconstructions associating with a reduction of the computational
efficiency. Overall, the current implicit method leads to an improvement in
efficiency over the explicit one in the cases with a large variation of mesh
size.Comment: arXiv admin note: text overlap with arXiv:2304.0948
Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes
In the previous studies, the high-order gas-kinetic schemes (HGKS) have
achieved successes for unsteady flows on three-dimensional unstructured meshes.
In this paper, to accelerate the rate of convergence for steady flows, the
implicit non-compact and compact HGKSs are developed. For non-compact scheme,
the simple weighted essentially non-oscillatory (WENO) reconstruction is used
to achieve the spatial accuracy, where the stencils for reconstruction contain
two levels of neighboring cells. Incorporate with the nonlinear generalized
minimal residual (GMRES) method, the implicit non-compact HGKS is developed. In
order to improve the resolution and parallelism of non-compact HGKS, the
implicit compact HGKS is developed with Hermite WENO (HWENO) reconstruction, in
which the reconstruction stencils only contain one level of neighboring cells.
The cell averaged conservative variable is also updated with GMRES method.
Simultaneously, a simple strategy is used to update the cell averaged gradient
by the time evolution of spatial-temporal coupled gas distribution function. To
accelerate the computation, the implicit non-compact and compact HGKSs are
implemented with the graphics processing unit (GPU) using compute unified
device architecture (CUDA). A variety of numerical examples, from the subsonic
to supersonic flows, are presented to validate the accuracy, robustness and
efficiency of both inviscid and viscous flows.Comment: arXiv admin note: text overlap with arXiv:2203.0904