Marek Brandner

Augmented Riemann solver for urethra flow modeling

In this paper we propose a new conservative numerical scheme for the male urethra and ureter fluid flow simulations. We use finite volume method based on technique of augmented system. Main goal is to construct such conservative scheme which maintains not only some special steady states but all possible ones. Furthermore this scheme should preserve non-negativity of essentially nonnegative quantities from their physical fundamental (here it is the cross-section of the urethra and ureter). Our scheme can be also modified to the high order scheme. At the end we present some numerical experiments.

Isogeometric analysis for turbulent flow

The article is devoted to the simulation of viscous incompressible turbulent fluid flow based on solving the Reynolds averaged Navier-Stokes (RANS) equations with different k-omega models. The isogeometrical approach is used for the discretization based on the Galerkin method. Primary goal of using isogeometric analysis is to be always geometrically exact, independent of the discretization, and to avoid a time-consuming generation of meshes of computational domains. For higher Reynolds numbers, we use stabilization SUPG technique in equations for k and omega. The solutions are compared with the standard benchmark example of turbulent flow over a backward facing step.

Numerical Schemes for Hyperbolic Balance Laws - Applications to Fluid Flow Problems

Balance laws arise from many areas of engineering practice specifically from the fluid mechanics. Many numerical methods for the solution of these balanced laws were developed in recent decades. The numerical methods are based on two views: solving hyperbolic PDE with a nonzero source term (the obvious description of the central and central-upwind schemes; (Kurganov & Levy, 2002; LeVeque, 2004)) or solving the augmented quasilinear nonconservative formulation (Gosse, 2001; Le Floch& Tzavaras, 1999; Pares, 2006). Furthermore, the methods can be interpreted using flux-difference splitting (or flux-vector splitting), or by selecting adaptive intervals and the transformation to the semidiscrete form (for example (Kurganov & Petrova, 2000)). We prefer the augmented quasilinear nonconservative formulation solved by the flux-difference splitting in our text. We try to formulate the methods in the most general form. The range of this text does not give the complete overview of currently used methods.

IgA-Based Solver for turbulence modelling on multipatch geometries

Abstract This paper is focused on numerical solving of RANS (Reynolds-Averaged Navier-Stokes) equation with k − ω model for simulation of turbulent flows in 3D. The solver which is based on a recently proposed approach called isogeometric analysis is presented. This numerical method is based on isoparametric approach, i.e., the same basis functions are used for the description of a geometry of a computational domain and also for the representation of a solution. As computational domains are described by NURBS objects in isogeometric analysis, any real application requires to handle the so-called multipatch domains, where the computational domain is composed of more parts and each part is represented by one NURBS object. In our solver, discontinuous Galerkin method is used to connect different NURBS patches into one computational domain. The results of the solver are demonstrated on a standard benchmark example – backward facing step.

High order well-balanced scheme for river flow modeling

We propose a new numerical scheme based on the finite volumes to simulate the river flow in the presence of a variable bottom surface. Our approach is based on the Riemann solver designed for the augmented quasilinear homogeneous formulation. The scheme has general semidiscrete wave-propagation form and can be extended to an arbitrary high order accuracy. The main goal is to construct the scheme, which is well-balanced, i.e. maintains not only some special steady states, but all steady states which can occur.

Nodal methods for a two-dimensional static multigroup diffusion calculation of nuclear reactors with hexagonal assemblies

Abstract This paper presents three variants of a hexagonal nodal method for determining neutron flux distribution in a nuclear reactor and its critical number. Their common framework constitutes the few-group, coarse-mesh finite-difference diffusion equations for all nodes inside the core domain. To achieve better accuracy without sacrificing efficiency, they are corrected by higher order nodal calculations formulated on pairs of nodes using the transverse integration procedure. This leads to three 1D equations coupled through neutron currents at transverse nodal boundaries. Approximation of the coupling has significant impact on the accuracy of transverse-integration based nodal methods and as such receives considerable attention. Three possibilities are discussed that define the variants of the developed nodal method. Once the transverse coupling term is suitably approximated, solution of nodal equations is computed semi-analytically by using an efficient node-by-node iterative procedure. The three implementations are compared on an example configuration of a VVER-1000 core.

Finite Volume Methods for Fluid Flow Through Elastic Tubes

There are two basic approaches towards solving this augmented system. The first one is based on componentwise methods – for example, the central schemes. We propose to use the semidiscrete version of these algorithms where the degenerate conservation law wt = 0 is solved exactly. The second approach is based on upwind schemes. If we use a finite volume method based on Roe’s linearization f(Uj+1)− f(Uj ) = Āj+1/2(Uj+1 −Uj ) where

High-resolution methods for two-component fluid flow problem with moving interface

This work is devoted to the numerical simulation of two--component fluid flow. Projection methods are used for solving the Navier-Stokes equations and high-resolution methods are used for solving the advection equation formulated for a volume fraction describing the location of the interface between the fluid components.

Numerical modelling of some two-phase fluid flow problems

Hydrodynamic (fluid flow) problems in general are actual from the wide points of view. The ecological catastrophe in the Czech Republic (2002), especially flooding of Pilsen, gives us new impulses for numerical simulation of particular fluid flow problems. Here we discuss two variants of mathematical fluid flow models: the multiphase compressible inviscid fluid flow model and the multi-component incompressible viscous fluid flow model.