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Showing 1 to 20 of 64 for “"finite difference methods"”.
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Seismic wave modelling using finite difference methods
… boundary conditions used to manufacture a finite computational domain. The Reynolds ABCs are found to be marginally better than Clayton-Engquist ABCs and are stable in all cases for our approach. We also adopt a scaling technique with variable grid geometry so as to extend the scope of the …
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Finite difference methods for the advection equation / Peter John Steinle
Bibliography : leaves 211-216
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Time-stable high-order finite difference methods for overset grids
… flexible framework for implementing high-order finite difference methods to simulate compressible viscous flows over complex geometries. Although overset methods have been widely used to solve time-dependent partial differential equations, very few proofs of stability exist for them. In …
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Finite-Difference Methods for the Wave Equation with Reduced Dispersion Errors
… in Finkelstein and Kastner (2007,2008) to derive finite-difference (FD) schemes in the joint time-space domain to reduce dispersion error. The key idea is that the true dispersion relation is satisfied exactly at some specified wavenum- bers. Liu and Sen (2009) further developed their idea, going …
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The application of high order finite difference methods to the diffusion-convection equation
… is approximated numerically with high order finite difference methods using five adjacent space node points by the Crank - Nicolson formulation. This method is referred to as the 5PFDM. It has fourth order correctness in space truncation error and shows good approximation to the solution of …
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ERROR BOUNDS OF COMPACT FINITE DIFFERENCE METHODS FOR SOME DISPERSIVE PDEs AND APPLICATIONS
… to propose and analyze some fourth-order compact finite difference schemes (4cFDs) for approximating several highly oscillatory dispersive PDEs, including the nonlinear Klein-Gordon equation in the nonrelativistic regime and the Zakharov system in the subsonic regime. Proofs of error estimate …
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High Order Immersed Finite Difference Methods for Complex Domains with Moving Boundaries and Interfaces
… restrictions on the interface motion. Immersed methods avoid these challenges by simulating moving geometries on a stationary Cartesian grid, locally altering the numerical method to account for boundaries and interfaces that are not grid-aligned. Most existing immersed methods have low-order …
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An accuracy study of central finite difference methods in second order boundary value problems
An accuracy study is made of central finite difference methods for solving boundary value problems which are governed by second order differential equations with variable coefficients leading to odd order derivatives. Three methods are studied through applications to selected problems. Definitive …
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Numerical Simulations of Stokes Flow by the Iterations of Boundary Conditions and Finite Difference Methods
… 2006) is used together with the well known Finite difference numerical method to solve the Stokes problem over a rectangular domain as well as in irregular domain. The iteration of boundary conditions method has been applied to the Stokes problem in a rectangular domain, 2 <x< 2 , d 2 < …
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Finite difference methods for 1st Order in time, 2nd order in space, hyperbolic systems used in numerical relativity
… is concerned with the development of numerical methods using finite difference techniques for the discretization of initial value problems (IVPs) and initial boundary value problems (IBVPs) of certain hyperbolic systems which are first order in time and second order in space. This type of system …
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Application of integral equation and finite difference methods to electromagnetic scattering by two-dimensional and body-of-revolution geometries
… are analyzed and some improvements to existing methods are presented. Some scattering problems involving two-dimensional and body of revolution geometries are solved using these techniques to demonstrate their capabilities and to point out their limitations.
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Scaling finite difference methods in large eddy simulation of jet engine noise to the petascale: numerical methods and their efficient and automated implementation
… requirements of CAA on numerical accuracy, finite difference methods in LES-based jet engine noise prediction rely on the implicitly formulated compact spatial partial differentiation and spatial filtering schemes, a crucial component of which is an embedded solver for tridiagonal linear …
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Efficient variable mesh techniques to solve interior layer problems
… This explains the need for approximation methods to gain some insight into the behaviour of the solution of such problems. Keeping this in mind, in this thesis we would like to explore a special class of numerical methods, namely, fitted finite difference methods to determine reliable …
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High Accuracy Fitted Operator Methods for Solving Interior Layer Problems
Fitted operator finite difference methods (FOFDMs) for singularly perturbed problems have been explored for the last three decades. The construction of these numerical schemes is based on introducing a fitting factor along with the diffusion coefficient or by using principles of the non-standard …
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Drum Sound Synthesis by Computer Simulation of the Wave Equation
… by computer solution of the wave equation using finite difference methods. The research is novel in that it takes into account the stiffness of the drumhead material, damping due to energy dissipation into the air and rim, mass loading of the air, and changing tension caused by stretching of the …
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Development of Advanced Nodal Diffusion Methods for Modern Computer Architectures
… multigroup advanced neutron diffusion nodal methods, ILLICO, have been implemented on sequential, vector, and vector-concurrent computers. Three dimensional realistic benchmark problems can be solved in vectorized mode in less than 0.73 s (33.86 Mflops) on a Cray X-MP/48. Vector-concurrent …
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Systems of Nonlinear Algebraic Equations Arising in Simulation of Semiconductor Devices
… model a semiconductor device. We use standard finite difference methods to discretize these equations and derive systems of nonlinear equations. Due to the extremely large number of unknowns it is prohibitively expensive to use Newton's method. However, the Jacobians of these systems are …
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A study on the effect of dilutions and buybacks on the pricing of equity and stock based claims using a finite difference mesh
… the total number of shares in issue. Then we use finite difference methods to investigate the differences in pricing options on a fixed portion of equity and options linked to the share price, as well as implications for American options on equity.
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Tavis Mining Highway Stability Study - Methods Overview and Sensitivity Study
… as a model comparison, using limit equilibrium methods, to one of the previous geotechnical studies performed at the mine. Finally, a sensitivity study of highwall stability is performed using finite difference methods.
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Krylov Subspace Spectral Methods with Non-homogenous Boundary Conditions
… this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their …
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