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Showing 1 to 16 of 16 for “"high order finite difference"”.
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Time-stable high-order finite difference methods for overset grids
… and 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. …
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High-Order Finite-Difference Schemes and Their Application to Computational Acoustics
… of this study is upon the numerical stability of high-order finite-difference schemes and their application to duct acoustics. Since acoustic waves are known to be non-dissipative and non-dispersive, high-order schemes are favored for their low dissipation and low dispersion relative to the …
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The application of high order finite difference methods to the diffusion-convection equation
… a porous medium 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 …
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Matched interface and boundary enhanced multiresolution time-domain algorithm for electromagnetic simulations
… method are conducted and compared with the high-order finite difference time-domain (FDTD) method . The proposed boundary treatment can also be applied to other high order approaches, such as the dispersion-relation-preserving (DRP) method. The MIB boundary scheme greatly enhances the …
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Direct numerical simulations of separated and separated-reattaching flows on massively parallel processing computers
… a flat plate held normal to a uniform stream. A high-order finite-difference formulation on collocated grids has been developed to perform unsteady fluid flow simulations in rectangular geometries. The numerical procedure is based on a fifth-order upwind-biased scheme for the convective terms and …
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Numerical Boundary Conditions for the Fourth -Order Accurate Finite -Difference Time -Domain Solution of Maxwell's Equations
… is the key to the proper implementation of high-order finite-difference time-domain (FDTD) methods for Maxwell's equations. In this dissertation, a new set of numerical boundary conditions at perfectly conducting walls and dielectric interfaces is proposed for Fang's fourth-order FDTD …
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Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations
… is devoted to develop a provably stable and high order approximation for the incompressible laminar boundary layer equations. A new set of energystable boundary conditions are derived using the energy method. It is shown that both the weak and strong implementation of these boundary …
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Performance analysis and optimization of a CFD application
… documents the analysis and optimization of a high-order finite difference computational fluid dynamics (CFD) application (PlasComCM). Performance bottlenecks were identified using performance tools and hardware counters. The performance analysis of PlasComCM showed that the quantity of memory …
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Large Eddy Simulation of Shear-Free Interaction of Homogeneous Turbulence with a Flat-Plate Cascade
… over a large number of plates (6-12 plates) in order to be able to represent numerically integral length scales on the order of blade-to-blade spacing. Having such a large number of solid surfaces in the simulation requires very large computational grid points to resolve the boundary layers on …
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High fidelity simulations of electrokinetic phenomena in microfluidic devices
… A multiblock in-house solver based on high-order finite difference schemes is developed to solve the system of equations and thus to numerically capture essential physics of ITP and EKI in microfluidic devices. Validation of the solver is provided for one-dimensional ITP problems in …
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Stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition
… is used. This is especially true for higher-order methods. To address this, high-order, provably stable, overlapping domain decomposition methods are derived for hyperbolic initial-boundary-value problems. The overlap is treated by splitting the domain into pieces and using newly …
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High Order Immersed Finite Difference Methods for Complex Domains with Moving Boundaries and Interfaces
… Most existing immersed methods have low-order spatial accuracy, requiring fine grids to generate accurate results. High order immersed methods can produce more accurate results at lower resolution, making them a promising tool for 3D simulations with tight error tolerances. However, the …
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Problems in cosmology and numerical relativity
… area of the thesis is the development a stable high order mesh refinement scheme for the solution of hyperbolic partial differential equations. It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. This …
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Cio-cio-san no yuutsu: memoirs of magnetogenesis and turbulent dynamo theory
… we make use of the PENCIL CODE, which is a high-order finite-difference Magnetohydrodynamical code capable of performing simulation runs in parallel using the Message Passing Interface (MPI) system for parallel processing. Theoretical results relevant to the simulations conducted are …
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Cio-cio-san no Yūutsu: memoirs of magnetogenesis and Turbulent Dynamo Theory
… we make use of the PENCIL CODE, which is a high-order finite-difference Magnetohydrodynamical code capable of performing simulation runs in parallel using the Message Passing Interface (MPI) system for parallel processing. Theoretical results relevant to the simulations conducted are …
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High order numerical methods applied to the analysis of transport phenomena in combustion
High order numerical methods present the desirable property of having much less error than second order methods for the same number of nodes, or degrees of freedom. This makes them very attractive for applications like computational acoustics and aeroacoustics, prediction of transition or direct …