On the long-time simulation accuracy of the discontinuous Galerkin method for 1D transport equation

Abstract: Unsteady corrector method is applied to study the DG method for 1D transport equation with constant velocity. Only smooth solutions are considered. On arbitrary non-uniform mesh we prove that the numerical error satisfies ||e|| = O(h(k+1)+ th(2k+1)) where k + 1 is the number of DOFs at one cell.Note: Research direction:Mathematical problems and theory of numerical method

Unsteady corrector method for accuracy analysis of linear semidiscrete schemes

Abstract: Unsteady corrector method is used to find the order of accuracy when it is greater than the order of truncation error and investigate the long-time evolution of solution error. In this paper this method is applied to linear semidiscrete schemes, which allows to simplify its description. We alsopresent its generalization for schemes with matrices next to temporal derivatives. Using this method we obtain new accuracy estimates for 4-point difference scheme R3.Note: Research direction:Mathematical problems and theory of numerical method

Implementation of the Flux Correction method on hybrid unstructured meshes

Abstract: Flux Correction method and its unsteady modification are the schemes originally proposed for solving Euler equations on simplicial meshes. In this paper we generalize these schemes for hybrid unstructured meshes using semitransparent control volumes and finite-element approach for gradient calculations. This modification preserves main properties of the original method, which is verified on test problems.Note: Research direction:Mathematical problems and theory of numerical method

Sound wave in an infinite circular cylinder in the presence of viscosity and heat conductivity

Abstract: In an infinite circular cylinder we consider exact solutions of the linearized Navier – Stokes equations for a heat conducting gas. No-slip conditions and constant temperature are imposed on the cylinder walls. We describe details of program implementation.Note: Research direction:Mathematical problems and theory of numerical method

On effective parallel implementation of vertex-centered schemes on sliding meshes

Abstract: Edge-based schemes are applied to gas dynamics simulation in rotor–stator systems usingsliding meshes. Numerical algorithm is presened. Multilevel MPI+OpenMP parallelization for cluster systems is described in detail.Note: Research direction:Programming, parallel computing, multimedi

EBR-WENO scheme for solving gas dynamics problems with discontinuities on unstructured meshes

Abstract: We develop EBR-WENO scheme for solving Euler equations on unstructured meshes. It belongs to the class of edge-based schemes with quasi-1D reconstruction of variables. The scheme monotonization is provided by using a convex conbination of three lower-order reconstructions of variables in a similar way as it is in the classical finite-difference WENO scheme. The new scheme damps oscillations near shocks on unstructured meshes and, due to its edge-based nature, requires rather low computational costs. The properties of the new scheme are demonstrated on several test problems.Note: Research direction:Mathematical problems and theory of numerical method

Edge-based Approximation of the Navier – Stokes equations for axial symmetric flows on unstructured meshes

Abstract: Considered are Navier – Stokes equations for axial symmetric flows of the viscous heat conducting ideal gas. Edge-based approximation on unstructured meshes are written. Compared are different approximations for the source term which models the asimuthal flux. The scheme is verified by test problems.Note: Research direction:Mathematical problems and theory of numerical method