A numerical study of SSP time integration methods for hyperbolic conservation laws

he method of lines approach for solving hyperbolic conservation laws is based on the idea of splitting the discretization process in two stages. First, the spatial discretization is performed by leaving the system continuous in time. This approximation is usually developed in a non-oscillatory manner with a satisfactory spatial accuracy. The obtained semi-discrete system of ordinary differential equations (ODE) is then solved by using some standard time integration method. In the last few years, a series of papers appeared, dealing with the high order strong stability preserving (SSP) time integration methods that maintain the total variation diminishing (TVD) property of the first order forward Euler method. In this work the optimal SSP Runge--Kutta methods of different order are considered in combination with the finite volume weighted essentially non-oscillatory (WENO) discretization. Furthermore, a new semi--implicit WENO scheme is presented and its properties in combination with different optimal implicit SSP Runge--Kutta methods are studied. Analysis is made on linear and nonlinear scalar equations and on Euler equations for gas dynamics

Numerical simulations of hydraulic transients in PHPP Fužine

U radu su provedene numeričke simulacije hidrauličkih tranzijenata u sustavu crpne hidroelektrane (CHE) Fužine pomoću nestacionarnog 1D modela strujanja pod tlakom u cijevi. Primjenom nekonzervativne formulacije modela nestacionarnog strujanja tekućine u cijevi pod tlakom i fluks-limitirane numeričke metode drugog reda postignuta je zadovoljavajuća točnost modela. Dobiveni numerički rezultati su pokazali dobro slaganje s izmjerenim podacima promatranog sustava.Hydraulic transients in pumping hydroelectric power plant (PHPP) Fužine were simulated with 1D unsteady pipe flow model. High accuracy of the model was accomplished with the use of nonconservative formulation of unsteady pipe flow model incorporating unsteady friction model and second order flux limited numerical scheme. Simulation results show very good agreement between the computed and measured piezometric heads, both in amplitude and frequency of the oscillation

Model šake s međuovisnim zglobovima za primjenu u rehabilitacijskoj robotici

Aim: This work presents a method for developing a simplified but efficient model of the complex human hand kinematics with the aim of its implementation in rehabilitation robotics. Material and methods: The approach incorporates modularity by simplifying the available model comprising 24 degrees of freedom (DOFs) to 9 DOFs, with the introduction of additional joint coupling parameters specific to different grasp types. The effect of dependent joints to the ranges-of-motion (ROMs) of the model is investigated and compared to the anatomical one. The index, middle, ring and little finger solutions to forward and inverse kinematics problems are then acquired. The implementation of the model, based on the median male bones dimensions, is made available in the open-source Robot Operating System (ROS) framework. Results: By including additional four inclination angles per finger, the devised kinematic hand model encompasses also finger curvatures, resulting in significant positioning accuracy improvements compared to the conventional model. The used 3D spatial position improvement metrics are the mean absolute (MAE) and mean relative errors (MRE). The dependent joint position MAEs range from 0.22 to 0.34 cm, while MREs range from 2.8 and 3.5 %, whereas the highest absolute and relative errors during fingertip positioning can reach 0.5 cm and 10.5 %, respectively. Conclusion: The performed investigation allowed establishing that by modelling finger curvature and assuring the adaptability of the model to a variety of human hands and rehabilitation modalities through joint dependency, represents the best approach towards a relatively simple and applicable rehabilitation model with functional human-like hand movements.Cilj: U radu se prezentira metoda za razvoj pojednostavljenog ali učinkovitog kinematičkog modela ljudske ruke koji će se implementirati u rehabilitacijskoj robotici. Materijali i metode: Pristup se temelji na pojednostavljenju postojećeg modela koji ima 24 stupnja slobode gibanja (DOF) na 9 DOF-a, uz uvođenje dodatnih konstrukcijskih parametara, specifičnih za različite vrste hvata. Nakon što je istražen utjecaj ovisnih zglobova na raspon pokreta (ROM) modela, te je isti uspoređen s anatomskim modelom, dobivena su rješenja problema inverzne i direktne kinematike kažiprsta, srednjeg prsta, prstenjaka i malog prsta. Implementacija modela, temeljena na dimenzijama muških kostiju koje odgovaraju medijanu muške populacije, ostvarena je pomoću programskog okruženja otvorenog koda Robot Operating System (ROS). Rezultati: Uzimanjem u obzir četiriju dodatnih kutova nagiba po prstu, razvijeni model ruke obuhvaća i zakrivljenost prstiju, što omogućuje povećanje točnosti pozicioniranja u usporedbi s konvencionalnim modelom. Kao mjerila za utvrđivanje povećanja točnosti prostornog pozicioniranja, korištene su srednja apsolutna greška (MAE) i srednja relativna greška (MRE). MAE se, ovisno o položaju zgloba, kreće od 0,22 do 0,34 cm, dok se MRE kreće od 2,8 do 3,5 %. Najveće apsolutne i relativne greške tijekom pozicioniranja vrha prsta mogu, pak, doseći 0,5 cm, odnosno 10,5 %. Zaključak: Zaključuje se da modeliranje zakrivljenosti prsta i osiguranje prilagodljivosti modela različitim pacijentima i rehabilitacijskim modalitetima kroz međuovisnost zglobova, predstavlja najbolji pristup dobivanju relativno jednostavnog, primjenjivog i funkcionalnog modela šake

Lie symmetry analysis and numerical solutions for thermo-solutal chemicallyreacting radiative micropolar flow from an inclined porous surface

Steady, laminar, incompressible thermo-solutal natural convection flow of micropolar fluid from an inclined perforated surface with convective boundary conditions is studied. Thermal radiative flux and chemical reaction effects are included to represent phenomena encountered in high-temperature materials synthesis operations. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Lie scaling group transformation is implemented to derive a self-similar form of the partial differential conservation equations. The resulting coupled nonlinear boundary value problem is solved with Runge-Kutta fourth order numerical quadrature (shooting technique). Validation of solutions with an optimized Adomian decomposition method algorithm is included. Verification of the accuracy of shooting is also conducted as a particular case of non-reactive micropolar flow from a vertical permeable surface. The evolution of velocity, angular velocity (micro-rotation component), temperature and concentration are examined for a variety of parameters including coupling number, plate inclination angle, suction/injection parameter, radiation-conduction parameter, Biot number and reaction parameter. Numerical results for steady state skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are tabulated and discussed. Interesting features of the hydrodynamic, heat and mass transfer characteristics are examined

Numerical Simulation of Hydraulic Transients in Rijeka HPP

In this work a new approach considering numerical modelling of waterhammer dissipation and attenuation is proposed. The classical Allievi liquid flow model has been extended with the Brunone unsteady friction model which includes separation of the local and convective unsteady friction factor. A widely-adopted approach in solving this model is treatment of the unsteady friction term as a classical source term, while the authors propose a non-conservative formulation, due to the existence of a non-conservative source term. The second order flux limited scheme is applied to the proposed formulation and is applied to simulations of transient flow in Rijeka HPP