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Showing 1 to 20 of 53 for “"Burgers Equation"”.
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A control problem for Burgers' equation
Burgers' equation is a one-dimensional simple model for convection-diffusion phenomena such as shock waves, supersonic flow about airfoils, traffic flows, acoustic transmission, etc. For high Reynolds number, the open-loop system (no control) produces steep gradients due to the nonlinear nature of …
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Finite element approximations of Burgers' equation
This work is a numerical study of Burgers' equation with Neumann boundary conditions. The goal is to determine the long term behavior of solutions. We develop and test two separate finite element and Galerkin schemes and then use those schemes to compute the response to various initial conditions …
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Control of Burgers' Equation With Mixed Boundary Conditions
… the problems of simulation and control for Burgers' equation with mixed boundary conditions. We first conduct numerical experiments to test the convergence and stability of two standard finite element schemes for various Robin boundary conditions and a variety of Reynolds numbers. These …
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Finite Element Approximations of Burgers' Equation with Robin's Boundary Conditions
This work is a numerical study of Burgers' equation with Robin's boundary conditions. The goal is to determine the behavior of the solutions in the limiting cases of Dirichlet and Neumann boundary conditions. We develop and test two separate finite element and Galerkin schemes. The …
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A Numerical Study of Burgers' Equation With Robin Boundary Conditions
This thesis examines the numerical solution to Burgers' equation on a finite spatial domain with various boundary conditions. We first conduct experiments to confirm the numerical solutions observed by other researchers for Neumann boundary conditions. Then we consider the case where the …
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Model Reduction of the Coupled Burgers Equation in Conservation Form
This thesis is a numerical study of the coupled Burgers equation. The coupled Burgers equation is motivated by the Boussinesq equations that are often used to model the thermal-fluid dynamics of air in buildings. We apply Finite Element Methods to the coupled Burgers equation and conduct several …
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Development of Discontinuous Galerkin Method for 1-D Inviscid Burgers Equation
… method to a classical partial differential equation to investigate the properties of the numerical solution and compare the numerical solution to the analytical solution by using discontinuous Galerkin method. This scheme is applied to 1-D non-linear conservation equation (Burgers equation) …
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Reduced Order Model Study of Burgers' Equation using Proper Orthogonal Decomposition
… we conduct a numerical study of the 1D viscous Burgers' equation and several Reduced Order Models (ROMs) over a range of parameter values. This study is motivated by the need for robust reduced order models that can be used both for design and control. Thus the model should first, allow for …
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Asymptotic properties of solutions of a KdV-Burgers equation with localized dissipation
We study the Korteweg-de Vries-Burgers equation. With a deep investigation into the spectral and smoothing properties of the linearized system, it is shown by applying Banach Contraction Principle and Gronwall's Inequality to the integral equation based on the variation of parameters formula and …
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A Numerical Method for solving the Periodic Burgers' Equation through a Stochastic Differential Equation
The Burgers equation, and related partial differential equations (PDEs), can be numerically challenging for small values of the viscosity parameter. For example, these equations can develop discontinuous solutions (or solutions with large gradients) from smooth initial data. Aside from numerical …
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Efficient Formulation of the Modified Nodal Integral Method and Development of Implicit, Explicit, and Multigrid Schemes Applied to the Two-Dimensional Burgers' Equation
Made available in DSpace on 2017-07-06T18:59:25Z (GMT). No. of bitstreams: 3 Wescott_Bradley_L_MS.pdf: 37261682 bytes, checksum: 07a50e858d2c887376e024b00579ea4e (MD5) Wescott_Bradley_L_MS_ABS.pdf: 705169 bytes, checksum: e042a4f022fb6236e683141b34fd34c1 (MD5) license.txt: 4813 bytes, checksum: …
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Residual-Based Discretization Error Estimation for Unsteady Flows
… flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is …
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On the Application of an Output-based Adaptive, Higher-order Finite Element Method to Sonic Boom Propagation
… validated using smooth solutions for the viscous Burgers equation and the adjoint PDE for a volume output functional. Additionally, artificial viscosity is incorporated via a shock sensor PDE approach to handle shock presence, with necessary corrections applied to the DWR error estimate. The …
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Improving shock-capturing robustness for higher-order finite element solvers
… Galerkin (DG) framework is used to discretize Burgers' equation and the Euler equations. Dissipation-based globalization methods are investigated using both a pre-defined continuation schedule and a variable continuation schedule based on homotopy methods, and Burgers' equation is used as a …
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Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems
… to problems governed by partial differential equations (PDEs). The method involves generating a numerical solution to the original problem of interest, curve fitting the solution, and generating source terms by operating the governing PDEs upon the curve fit. Adding these source terms to the …
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Filter Based Stabilization Methods for Reduced Order Models of Convection-Dominated Systems
… They are tested in the numerical setting of Burgers equation, a nonlinear, time dependent problem with one spatial dimension. Regularization is considered for the low viscosity, convection dominated setting.
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The dynamics of steady supersonic dense gas flows
… design. The weak shock development results in a Burgers equation which is then solved numerically using the well-known MacCormack scheme. The results include the demonstration of many non-classical results such as expansion shocks, compression fans, shock-splitting and shock-fan combinations. …
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Approximate Deconvolution Reduced Order Modeling
… the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient ( ν= 10⁻³).
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A dynamic multiscale viscosity algorithm for shock capturing in Runge Kutta Discontinuous Galerkin methods
… 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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