Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 19 of 19 for “"hyperbolic equations"”.
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A DG HWENO scheme for hyperbolic equations
… finite element solver for the nonlinear Euler equations of gas dynamics, we develop a shock capturing scheme for hyperbolic equations. The Hermite Weighted Essentially Non-Oscillatory (HWENO) methodology introduced by Qiu [10, 14] is used as the starting point for the proposed limiter. We …
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Ghost-point methods for Elliptic and Hyperbolic Equations
In questa tesi abbiamo presentato un metodo ghost-point alle differenze finite per la risoluzione numerica delle equazioni ellittiche e iperboliche su domini arbitrari. Le equazioni sono discretizzate su una griglia Cartesiana regolare. In un primo momento abbiamo applicato il metodo Coco-Russo, …
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A dynamic multiscale viscosity algorithm for shock capturing in Runge Kutta Discontinuous Galerkin methods
… shock capturing procedure has been developed for hyperbolic equations. The Dynamic Multiscale Viscosity method, originally presented by Oberai and Wanderer [8, 9] in a Fourier Galerkin context, is adapted to the Discontinuous Galerkin discretization. The notions of diffusive model term, artificial …
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A novel state-space based method for direct numerical simulation of particle-laden turbulent flows
… method. The method generates the governing equations for the parameters of the kernel density functions. The resulting system of hyperbolic equations are solved using a high-order accurate numerical method for non-conservative hyperbolic equations. The numerical framework results in an …
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Numerical detection of complex singularities in two and three dimensions
… often occur in solutions to partial differential equations; important examples include the formation of shock fronts in hyperbolic equations and self-focusing type blow up in nonlinear parabolic equations. Information about formation and structure of singularities can have significant role in …
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An analysis of the TR-BDF2 integration scheme
… of coupled non-linear partial differential equations (PDEs). It was originally Professor KlausJiirgen Bathe who suggested that further analysis was needed in this area. We draw attention to numerical instabilities that arise due to insufficient numerical damping from the Crank-Nicolson …
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Global normal forms and global properties in function spaces for second order Shubin type operators
… problems on Rn globally in time for second order hyperbolic equations P(x;D)+R(x;D), where P(x;D) is a second or der self-adjoint globally elliptic Shubin pseudodifferential operator and R(x;D) is a first order pseudodifferential operator.
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Elongational Flows in Polymer Processing
… technique. In this work, we shall discuss the equations of melt-spinning in viscous and viscoelastic flow. These quasilinear hyperbolic equations model the uniaxial extension of a fluid thread before its solidification. We will address the following topics: first we shall prove existence, …
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Development of a flow-condition-based interpolation 9-node element for incompressible flows
The Navier-Stokes equations are widely used for the analysis of incompressible laminar flows. If the Reynolds number is increased to certain values, oscillations appear in the finite element solution of the Navier-Stokes equations. In order to solve for high Reynolds number flows and avoid the …
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Physics motivated algorithms for partial differential equations
… idea will be illustrated in terms of solvers for hyperbolic equations, such as those describing advection in fluids and linear wave propagation. We demonstrate in this thesis that a conscious pursuit of physics essence can lead to useful numerical algorithms. From this point of view, the …
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Evaluation of TDOA Techniques for Position Location in CDMA Systems
… time difference estimates and for solving the hyperbolic equations generated by those estimates has been made. This research also considers a measure of accuracy for TDOA position location method which is shown to be more suitable for CDMA systems and more closely matches to the FCC …
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STRUCTURE-OPTIMIZED AND ORDER-PRESERVING METHODS FOR ADVECTION AND TIME STEPPING
… in computational methods for differential equations by developing novel high-order accurate numerical schemes that can apply to multi-physics or multi-scale problems. Motivated by the need for numerical methods with long-time accurate solutions in complex advection-dominated problems, we …
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Development of a 20-moment Polydisperse and Polykinetic Spray Model Coupled With a Surface Density Approach for the Modelling of the Dense and Disperse Liquid Spray Regimes
… and introduces two additional scalar transport equations for the liquid mass fraction and mass-weighted liquid-gas surface density. In this fully Eulerian treatment, spray atomization is modelled through the imposition of source terms in the two transport equations which represent the key …
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Mathematical Modeling and Computational Studies for Cell Signaling
… steady states from simulating differential equations to finding the roots of polynomials, of which the degree depends on the number of phosphorylation sites N. In the next problem, we developed a generic mathematical model to incorporate MAPK cascade with two substrates in the presence of …
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New efficient contact discontinuity capturing techniques in supersonic flow simulations
… algorithms for solving systems of nonlinear hyperbolic equations are considered. The issues of the capturing and the non-diffusive resolution of contact discontinuities were investigated using two different approaches: a kinetic fluctuation splitting scheme and a discontinuity confinement …
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Development of Discontinuous Galerkin Method for 1-D Inviscid Burgers Equation
… simplified model of the inviscid Navier-stokes equations. In this work three cases are studied. They are sinusoidal wave profile, initial shock discontinuity and initial linear distribution. A grid and time step refinement is performed. Riemann fluxes at each element interfaces are calculated. …
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Two-phase two-fluid model solver based on a high-resolution total variation diminishing scheme
… The new scheme is derived first for scalar hyperbolic problems using the method of flux limiters, then extended to the two-phase two-fluid model. A hybridization of the monotone 1st-order upwind scheme and the Quadratic Upstream Interpolation scheme (QUICK) is implemented using a new flux …
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A unified multi-physics formulation for combustion modelling
… simultaneous solution of appropriate systems of equations for the behaviour of the condensed-phase explosive and the elastoplastic response of the confiners. In the present work, we employ a mathematical model proposed by Peshkov and Romenski, which unifies fluid and solid mechanics by means of …