TY - JOUR

T1 - A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations

AU - Karagiozis, K.

AU - Kamakoti, R.

AU - Pantano, C.

N1 - Funding Information:
This work was supported in part by DOE/PECASE award LLNL B574743 and by NASA NRA award NNX08AL31A (University of Minnesota is prime). The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the DOE, NASA or the US Government.

PY - 2010/2/1

Y1 - 2010/2/1

N2 - A numerical method to solve the compressible Navier-Stokes equations around objects of arbitrary shape using Cartesian grids is described. The approach considered here uses an embedded geometry representation of the objects and approximate the governing equations with a low numerical dissipation centered finite-difference discretization. The method is suitable for compressible flows without shocks and can be classified as an immersed interface method. The objects are sharply captured by the Cartesian mesh by appropriately adapting the discretization stencils around the irregular grid nodes, located around the boundary. In contrast with available methods, no jump conditions are used or explicitly derived from the boundary conditions, although a number of elements are adopted from previous immersed interface approaches. A new element in the present approach is the use of the summation-by-parts formalism to develop stable non-stiff first-order derivative approximations at the irregular grid points. Second-order derivative approximations, as those appearing in the transport terms, can be stiff when irregular grid points are located too close to the boundary. This is addressed using a semi-implicit time integration method. Moreover, it is shown that the resulting implicit equations can be solved explicitly in the case of constant transport properties. Convergence studies are performed for a rotating cylinder and vortex shedding behind objects of varying shapes at different Mach and Reynolds numbers.

AB - A numerical method to solve the compressible Navier-Stokes equations around objects of arbitrary shape using Cartesian grids is described. The approach considered here uses an embedded geometry representation of the objects and approximate the governing equations with a low numerical dissipation centered finite-difference discretization. The method is suitable for compressible flows without shocks and can be classified as an immersed interface method. The objects are sharply captured by the Cartesian mesh by appropriately adapting the discretization stencils around the irregular grid nodes, located around the boundary. In contrast with available methods, no jump conditions are used or explicitly derived from the boundary conditions, although a number of elements are adopted from previous immersed interface approaches. A new element in the present approach is the use of the summation-by-parts formalism to develop stable non-stiff first-order derivative approximations at the irregular grid points. Second-order derivative approximations, as those appearing in the transport terms, can be stiff when irregular grid points are located too close to the boundary. This is addressed using a semi-implicit time integration method. Moreover, it is shown that the resulting implicit equations can be solved explicitly in the case of constant transport properties. Convergence studies are performed for a rotating cylinder and vortex shedding behind objects of varying shapes at different Mach and Reynolds numbers.

KW - Centered finite-differences

KW - Compressible Navier-Stokes equations

KW - Immersed interface method

KW - Non-dissipative methods

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U2 - 10.1016/j.jcp.2009.10.005

DO - 10.1016/j.jcp.2009.10.005

M3 - Article

AN - SCOPUS:70449697850

VL - 229

SP - 701

EP - 727

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 3

ER -