Analysis of upwind and high‐resolution schemes for solving convection dominated problems in porous media

The conservation laws governing the multiphase flows in porous media are often convection‐dominated and have a steep fronts that require accurate resolution. Standard discretization methods of the convection terms do not perform well for such problems. The main aim of this work is to analyze the use of upwind and high‐ resolution schemes in such cases. First, we use a first differential approximation method to perform a theoretical analysis of a standard upwind approximation and different time stepping schemes for the linear hyperbolic equations in 1‐ and 2D. Next, we present a popular approach to reduce the amount of numerical diffusion introduced by upwind approximation ‐ high‐resolution schemes. We compare our implementation of one of the recently proposed central‐upwind schemes against the upwind schemes on several test problems based on Buckley‐Leverett equation and discuss the results. Finally, a parallel version of central‐upwind scheme in 2D is presented. It was implemented using our C++ library of parallel arrays ‐ ParSol. First Published Online: 14 Oct 201

The finite difference scheme for mathematical modeling of wood drying process

This work discusses issues on the design of finite difference schemes for modeling the moisture movement process in the wood. A new finite difference scheme is proposed. The stability and convergence in the maximum norm are proved for different types of boundary conditions. Medienos džiovinimo uždavinio sprendimas baigtinių skirtumų metodu Santrauka Šiame darbe sprendžiama dvieju diferencialiniu lygčiu sistema, kuri aprašo ivairius procesus, svarbius pramoneje, ekologijoje, technikoje. Tokiu uždaviniu pavyzdžiai yra medienos džiovinimo procesas, upiu taršos koncentracijos modeliavimas ir kiti. Darbe sudaryta baigtiniu skirtumu schema, kurios sprendinys yra monotoniška funkcija, o realizacijos algoritmas ‐ ekonomiškas. Ištirtas tokios baigtiniu skirtumu schemos stabilumas maksimumo normoje ir irodyta, kad schema yra nesalygiškai stabili pirmojo, antrojo ir trečiojo tipo kraštiniu salygu atvejais. Pateikta konvergavimo irodymo metodikos modifikacija, leidžianti pagristi didesni diskrečiojo sprendinio tiksluma, kai matematiniame modelyje nera konvekcijos nario. First Published Online: 14 Oct 201

Mathematical modeling of wood drying process

This work focuses on the development of mathematical models describing moisture movement in wood, when the wood is considered as porous medium. Main moisture transport mechanisms are discussed. It is shown how the wood can be described as a two‐ or three‐phase system. Summaries of several multiphase flow models are presented in the hierarchical order: from the most general models to more simple examples. The approximation steps are described explicitly, and all assumptions are given in detail. It shown how models for specific applications in wood drying or saturation can be obtained. Medienos džiovinimo proceso matematiniai modeliai Santrauka. Šiame straipsnyje pagrindinis dėmesys skiriamas drėgmes koncentracijos kitimo medienoje matematiniam modeliavimui, kai mediena yra nagrinėjama kaip poringa terpė. Yra aptarti pagrindiniai skysčių judėjimo mechanizmai, naudojant dvifazius ir trifazius artinius. Sudaryta hierarchinė modelių sistema, apimanti tiek pačius bendriausius modelius, tiek ir jų supaprastintus variantus. Visi modelių išvedimo žingsniai aprašomi išreikštiniu būdu, griežtai suformuluotos tokių modelių teisingumo prielaidos. Parodyta, kad esant tam tikroms sąlygoms iš šių modeliu galime gauti gerai žinomus artinius, teoriškai pagristos jų koeficientų išraiškos. First Published Online: 14 Oct 201

A NOVEL SIMPLE-BASED PRESSURE-ENTHALPY COUPLING SCHEME FOR ENGINE FLOW PROBLEMS

A novel method in CFD derived from the SIMPLE algorithm is presented. Instead of solving the linear equations for each variable and the pressurecorrection equation separately in a so-called segregated manner, it relies on the solution of a linear system that comprises the discretisation of enthalpy and pressurecorrection equation which are linked through physical coupling terms. These coupling terms reflect a more accurate approximation of the density update with respect to thermodynamics (compared to standard SIMPLE method). We show that the novel method is a reasonable extension of existing CFD techniques for variable density flows based on SIMPLE. The novel method leads to a reduction of the number of iterations of SIMPLE which translates in many – but not in all – cases to a reduction in computing time. We will therefore demonstrate practical advantages and restrictions in terms of computational efficiency for industrial CFD applications in the field of piston engine simulations