TY - GEN
T1 - Very high-order accurate sharp immersed interface method
T2 - 23rd AIAA Computational Fluid Dynamics Conference, 2017
AU - Hosseinverdi, Shirzad
AU - Fasel, Hermann F.
N1 - Publisher Copyright:
© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.
PY - 2017
Y1 - 2017
N2 - Development of robust and very high-order accurate Immersed Interface Method (IIM) for solving the incompressible Navier-Stokes equations in the vorticity-velocity formulation on non-equidistant grids is presented. For computation of spatial derivatives on regular grid points, a seventh-order upwind combined compact difference (CCD) scheme for firstderivative and sixth-order central CCD scheme for second derivative are employed. The coefficients of the CCD schemes are constructed for a non-equidistant grid instead of using a coordinate transformation. Corrections to the finite difference schemes are used for irregular grid points near the interface of the immersed boundary to maintain high formal accuracy. For the interface points, the CCD schemes are tuned and adjusted accordingly to obtain numerically stable schemes and no jump correction will therefore be required. To demonstrate the numerical stability of the new IIM, both semi- and fully-discrete eigenvalue problems are employed for the one-dimensional pure advection (inviscid) and the pure diffusion, and advection-diffusion equations. The new IIM satisfies both necessary and sufficient conditions for numerical stability. The new IIM was first applied to two-dimensional linear advection equation to demonstrate its stability. Then the development of a new, efficient and high-order sharp-interface method for the solution of the Poisson equation in irregular domains on non-equidistant grids is presented. The underlying approach for this is based on the combination of the fourth-order compact finite difference scheme and the multiscale multigrid (MSMG) method. The computational efficiency of the new solution strategy for the Poisson equation is demonstrated with regard to convergence rate and required computer time, which shows that the MSMG method is equally efficient for domains with immersed boundaries and for simple domains. To validate the application of IIM for incompressible flows, the results from the new method is compared with the benchmark solutions for the flow past a circular cylinder and the propagation of Tollmien-Schlichting wave in a boundary layer.
AB - Development of robust and very high-order accurate Immersed Interface Method (IIM) for solving the incompressible Navier-Stokes equations in the vorticity-velocity formulation on non-equidistant grids is presented. For computation of spatial derivatives on regular grid points, a seventh-order upwind combined compact difference (CCD) scheme for firstderivative and sixth-order central CCD scheme for second derivative are employed. The coefficients of the CCD schemes are constructed for a non-equidistant grid instead of using a coordinate transformation. Corrections to the finite difference schemes are used for irregular grid points near the interface of the immersed boundary to maintain high formal accuracy. For the interface points, the CCD schemes are tuned and adjusted accordingly to obtain numerically stable schemes and no jump correction will therefore be required. To demonstrate the numerical stability of the new IIM, both semi- and fully-discrete eigenvalue problems are employed for the one-dimensional pure advection (inviscid) and the pure diffusion, and advection-diffusion equations. The new IIM satisfies both necessary and sufficient conditions for numerical stability. The new IIM was first applied to two-dimensional linear advection equation to demonstrate its stability. Then the development of a new, efficient and high-order sharp-interface method for the solution of the Poisson equation in irregular domains on non-equidistant grids is presented. The underlying approach for this is based on the combination of the fourth-order compact finite difference scheme and the multiscale multigrid (MSMG) method. The computational efficiency of the new solution strategy for the Poisson equation is demonstrated with regard to convergence rate and required computer time, which shows that the MSMG method is equally efficient for domains with immersed boundaries and for simple domains. To validate the application of IIM for incompressible flows, the results from the new method is compared with the benchmark solutions for the flow past a circular cylinder and the propagation of Tollmien-Schlichting wave in a boundary layer.
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U2 - 10.2514/6.2017-3624
DO - 10.2514/6.2017-3624
M3 - Conference contribution
AN - SCOPUS:85088408665
SN - 9781624105067
T3 - 23rd AIAA Computational Fluid Dynamics Conference, 2017
BT - 23rd AIAA Computational Fluid Dynamics Conference, 2017
PB - American Institute of Aeronautics and Astronautics Inc, AIAA
Y2 - 5 June 2017 through 9 June 2017
ER -