Search results for "Euler method"

showing 6 items of 6 documents

On numerical simulation of the continuous casting process

1988

In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.

Continuous castingSurface (mathematics)Nonlinear systemMaterials scienceComputer simulationGeneral MathematicsHeat transferMultiphase heat transferGeneral EngineeringCalculusBoundary value problemMechanicsBackward Euler methodJournal of Engineering Mathematics
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ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS

2010

In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.

Dynamical systems theoryApplied MathematicsModeling and SimulationLattice (order)AttractorMathematical analysisLimit setRandom dynamical systemEngineering (miscellaneous)Backward Euler methodNon-Newtonian fluidMathematicsLinear dynamical systemInternational Journal of Bifurcation and Chaos
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Zero Viscosity Limit for Analytic Solutions, of the Navier-Stokes Equation on a Half-Space.¶I. Existence for Euler and Prandtl Equations

1998

This is the first of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space. In this paper we prove short time existence theorems for the Euler and Prandtl equations with analytic initial data in either two or three spatial dimensions. The main technical tool in this analysis is the abstract Cauchy-Kowalewski theorem. For the Euler equations, the projection method is used in the primitive variables, to which the Cauchy-Kowalewski theorem is directly applicable. For the Prandtl equations, Cauchy-Kowalewski is applicable once the diffusion operator in the vertical direction is inverted.

Laplace's equationIndependent equationSemi-implicit Euler methodPrandtl numberMathematical analysisMathematics::Analysis of PDEsStatistical and Nonlinear PhysicsBackward Euler methodEuler equationsPhysics::Fluid DynamicsEuler methodsymbols.namesakeEuler's formulasymbolsMathematical PhysicsMathematicsCommunications in Mathematical Physics
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DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

1998

Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given. First Published Online: 14 Oct 2010

Mathematical analysisMathematicsofComputing_NUMERICALANALYSISNumerical methods for ordinary differential equationsExplicit and implicit methods-Backward Euler methodModeling and SimulationCollocation methodQA1-939Crank–Nicolson methodDifferential algebraic equationMathematicsAnalysisMathematicsMatrix methodNumerical partial differential equationsMathematical Modelling and Analysis
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Analysis of a Parabolic Cross-Diffusion Semiconductor Model with Electron-Hole Scattering

2007

The global-in-time existence of non-negative solutions to a parabolic strongly coupled system with mixed Dirichlet–Neumann boundary conditions is shown. The system describes the time evolution of the electron and hole densities in a semiconductor when electron-hole scattering is taken into account. The parabolic equations are coupled to the Poisson equation for the electrostatic potential. Written in the quasi-Fermi potential variables, the diffusion matrix of the parabolic system contains strong cross-diffusion terms and is only positive semi-definite such that the problem is formally of degenerate type. The existence proof is based on the study of a fully discretized version of the system…

Parabolic cylindrical coordinatesApplied MathematicsDegenerate energy levelsMathematical analysisBoundary value problemParabolic cylinder functionPoisson's equationGalerkin methodParabolic partial differential equationBackward Euler methodAnalysisMathematicsCommunications in Partial Differential Equations
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Optimal Heating of an Indoor Swimming Pool

2020

This work presents the derivation of a model for the heating process of the air of a glass dome, where an indoor swimming pool is located in the bottom of the dome. The problem can be reduced from a three dimensional to a two dimensional one. The main goal is the formulation of a proper optimization problem for computing the optimal heating of the air after a given time. For that, the model of the heating process as a partial differential equation is formulated as well as the optimization problem subject to the time-dependent partial differential equation. This yields the optimal heating of the air under the glass dome such that the desired temperature distribution is attained after a given…

implicit Euler methodWork (thermodynamics)Optimization problemfinite element methodlämmitysjärjestelmät010103 numerical & computational mathematics01 natural sciences010305 fluids & plasmasDome (geology)0103 physical sciencesprojected gradient method0101 mathematicsMathematicsosittaisdifferentiaaliyhtälötPartial differential equationheat equationNumerical analysisProcess (computing)Mechanicsmatemaattinen optimointiOptimal controlelementtimenetelmäsovellettu matematiikkaPDE-constrained optimizationnumeerinen analyysicontrol constraintsmatemaattiset mallitGradient method
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