Search results for "Simulation."
showing 10 items of 4779 documents
Chebyshev’s Method on Projective Fluids
2020
We demonstrate the acceleration potential of the Chebyshev semi-iterative approach for fluid simulations in Projective Dynamics. The Chebyshev approach has been successfully tested for deformable bodies, where the dynamical system behaves relatively linearly, even though Projective Dynamics, in general, is fundamentally nonlinear. The results for more complex constraints, like fluids, with a particular nonlinear dynamical system, remained unknown so far. We follow a method describing particle-based fluids in Projective Dynamics while replacing the Conjugate Gradient solver with Chebyshev’s method. Our results show that Chebyshev’s method can be successfully applied to fluids and potentially…
Fine-Mesh Numerical Simulations for 2D Riemann Problems with a Multilevel Scheme
2001
The numerical simulation of physical problems modeled by systems of conservation laws can be difficult due to the occurrence of discontinuities and other non-smooth features in the solution.
Approximate Lax–Wendroff discontinuous Galerkin methods for hyperbolic conservation laws
2017
Abstract The Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in general more compact and efficient than RKDG methods of comparable order of accuracy, the formulation of LWDG methods involves the successive computation of exact flux derivatives. This procedure allows one to construct schemes of arbitrary formal order of accuracy in space and time. A new approximation procedure avoids the computation of ex…
Adaptive mesh refinement techniques for high-order shock capturing schemes for multi-dimensional hydrodynamic simulations
2006
The numerical simulation of physical phenomena represented by non-linear hyperbolic systems of conservation laws presents specific difficulties mainly due to the presence of discontinuities in the solution. State of the art methods for the solution of such equations involve high resolution shock capturing schemes, which are able to produce sharp profiles at the discontinuities and high accuracy in smooth regions, together with some kind of grid adaption, which reduces the computational cost by using finer grids near the discontinuities and coarser grids in smooth regions. The combination of both techniques presents intrinsic numerical and programming difficulties. In this work we present a …
Flotation with sedimentation: Steady states and numerical simulation of transient operation
2020
Abstract A spatially one-dimensional model of the hydrodynamics of a flotation column is based on one continuous phase, the fluid, and two disperse phases: the aggregates, that is, bubbles with attached hydrophobic valuable particles, and the solid particles that form the gangue. A common feed inlet for slurry mixture and gas is considered and the bubbles are assumed to be fully aggregated with hydrophobic particles as they enter the column. The conservation law of the three phases yields a model expressed as a system of partial differential equations where the nonlinear constitutive flux functions come from the drift-flux and solids-flux theories. In addition, the total flux functions are …
The exact finite‐difference scheme for vector boundary‐value problems with piece‐wise constant coefficients
1998
We will consider the exact finite‐difference scheme for solving the system of differential equations of second order with piece‐wise constant coefficients. It is well‐known, that the presence of large parameters at first order derivatives or small parameters at second order derivatives in the system of hydrodynamics and magnetohydrodynamics (MHD) equations (large Reynolds, Hartmann and others numbers) causes additional difficulties for the applications of general classical numerical methods. Thus, important to work out special methods of solution, the so‐called uniform converging computational methods. This gives a basis for the development of special monotone finite vector‐difference schem…
Dynamic analysis for axially moving viscoelastic panels
2012
In this study, stability and dynamic behaviour of axially moving viscoelastic panels are investigated with the help of the classical modal analysis. We use the flat panel theory combined with the Kelvin–Voigt viscoelastic constitutive model, and we include the material derivative in the viscoelastic relations. Complex eigenvalues for the moving viscoelastic panel are studied with respect to the panel velocity, and the corresponding eigenfunctions are found using central finite differences. The governing equation for the transverse displacement of the panel is of fifth order in space, and thus five boundary conditions are set for the problem. The fifth condition is derived and set at the in-…
Long-range cohesive interactions of non-local continuum faced by fractional calculus
2008
Abstract A non-local continuum model including long-range forces between non-adjacent volume elements has been studied in this paper. The proposed continuum model has been obtained as limit case of two fully equivalent mechanical models: (i) A volume element model including contact forces between adjacent volumes as well as long-range interactions, distance decaying, between non-adjacent elements. (ii) A discrete point-spring model with local springs between adjacent points and non-local springs with distance-decaying stiffness connecting non-adjacent points. Under the assumption of fractional distance-decaying interactions between non-adjacent elements a fractional differential equation in…
Fractional visco-elastic Euler–Bernoulli beam
2013
Abstract Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some c…
Estimation of recombinant protein production in Pichia pastoris base don a constraint-based model
2012
[EN] A previously validated constraint based model and possibilistic MFA have been used to design a simple estimator of protein production rate in Pichia pastoris cultures. A structured model of the yeast P. pastoris metabolism is used to predict the balance of key energetic equivalents such as ATP from available measurements, mainly substrate consumption, gases exchange rates and biomass specific growth. It has been shown that ATP flux can be related to biomass growth and protein productivity specific rates by linear regression. Cross-validation has been applied for robust parameter fitting on the basis of chemostat, steady-state experimental conditions. In this way, protein estimation can…