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On the dependence on parameters for second order discrete boundary value problems with the p(k)-Laplacian

Smejda J., Wieteska R.

Opuscula Mathematica

2014

Vol. 34, no. 4

851--870

In this paper we study the existence and the nonexistence of solutions for the boundary value problems of a class of nonlinear second-order discrete equations depending on a parameter. Variational (the mountain pass technique) and non-variational methods are applied.

Third-order method for simulation of compressible flows

Wieteska R., Rokicki J.

Archives of Mechanics

2008

Vol. 60, nr 6

491-507

The paper discusses finite volume WENO reconstruction applied to simulation of compressible 3D Euler flows. The main objective of this work is presentation of the new reconstruction procedure (third-order of accuracy in space), together with the procedure for integration of numerical fluxes applied to simulations of compressible 3D Euler flows, using unstructured meshes.

Investigation of WENO schemes for 3D unstructured grids

Wieteska R., Majewski J., Rokicki J.

Computer Assisted Mechanics and Engineering Sciences

2007

Vol. 14, No. 3

457-470

This paper paper discusses accuracy of WENO reconstruction used for unstructured grids and applied to two common discretization approaches within Finite Volume Method (FVM). They are Cell Centered and Vertex Centered methods. The numerical results are shown for 3D supersonic flow in a channel and for ONERA M6 wing. The comparison of computational performance of both methods is included.

Third-order WENO method on 3D unstructured tetrahedral mesches

Rokicki J., Wieteska R.

Systems : journal of transdisciplinary systems science

2006

Vol. 11, nr 1

74-85

The paper discusses finite volume WENO reconstruction applied to simulation of compressible 3D Euler flows using unstructured tetrahedral meshes. The main point of interest is the case when the mesh becomes highly irregular or stretched. Special transformation is used in such cases to recover the third-order accuracy of reconstruction. This transformation has to be locally applied to each stencil on which the reconstruction is sought. This procedure is verified first on a sequence of 3D meshes in a unit cube. The performance of the full algorithm (including the extended nonlinear weighing) is verified for the 3D subsonic and transonic flows in a channel with smooth sinusoidal bump.