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.
Results
Showing 1 to 15 of 15 for “"hyperbolic conservation laws"”.
-
Optimal and Feedback Control for Hyperbolic Conservation Laws
This dissertation studies hyperbolic partial differential equations for Conservation Laws motivated by traffic control problems. New traffic models for multi-directional flow in two dimensions are derived and their properties studied. Control models are proposed where the control variable is a …
-
High Order Fluctuation Splitting Schemes for Hyperbolic Conservation Laws
… discretisation for the solution of steady conservation laws on unstructured meshes. This is an alternative approach to the two existing higher than second order fluctuation splitting schemes, which use submesh reconstruction (developed by Abgrall and Roe) and gradient recovery (developed by …
-
A Spacetime Discontinuous Galerkin Method for Hyperbolic Conservation Laws
The basic SDG approximation is a simple Bubnov-Galerkin projection that is not prone to global patterns of spurious oscillations. However, it does require stabilization to eliminate local overshoot and undershoot in the immediate vicinity of shocks and other discontinuous solution features. We …
-
Invariant-region-preserving discontinuous Galerkin methods for systems of hyperbolic conservation laws
… discontinuous Galerkin (DG) schemes solving hyperbolic conservation law systems. In particular, our focus is on designing an IRP limiter to modify the numerical solution and identifying sufficient conditions for IRP DG schemes by extending Zhang and Shu's work on positivity-preserving schemes …
-
Semi-implicit schemes for compressible fluids in elastic pipes and a-posteriori sub-cell finite volume limiting techniques for semi-implicit Discontinuous Galerkin schemes for hyperbolic conservation laws on staggered meshes
… of partial differential equations (PDE) for hyperbolic conservation laws using semi-implicit numerical methods on staggered meshes applied both to the class of finite volume (FV) and both to the family of high order Discontinuous Galerkin (DG) finite elements schemes. In particular, we want …
-
Error estimates for numerical approximations to scalar conservation laws
… certain finite volume approximations of scalar hyperbolic conservation laws. <br>We introduce a new technique to prove a-priori error estimates which is based <br>on a duality argument and involves a consistency error of cell averages. <br>Next, we generalize finite volume schemes on staggered …
-
Mathematical modeling of shock induced martensitic phase transitions
… doing this, a new numerical method for nonlinear hyperbolic conservation laws with phase transitions is developed. Furthermore, in order to improve the quantitative agreement with experiments, several extensions of the Bruno-Vaynblat model are introduced and studied. These include the addition of …
-
Accelerating The Discontinuous Galerkin Cell-Vertex Scheme (Dg-Cvs) Solver On Cpu-Gpu Heterogeneous Systems
… accurate and robust numerical solver for general hyperbolic conservation laws. It can solve a broad range of conservation laws such as the shallow water equation and Magnetohydrodynamics equations. Dg-Cvs is a Riemann-Solver-free high order space-time method for arbitrary space conservation laws. …
-
Large Time Step and Overlapping Grids for Conservation Laws
… Method for computing numerical solutions to hyperbolic systems of conservation laws. We also consider a method of overlapping spatial grids for which variants have proved to be an important consideration in large scale applications. In practice we often run into grids which have a fairly …
-
A dimensionally split Cartesian cut cell method for Computational Fluid Dynamics
… cell problem' when computing solutions for hyperbolic conservation laws by combining wave speed and geometric information to develop a novel stabilised cut cell flux. The convergence and stability of the developed technique are proved for the one-dimensional linear advection equation, while …
-
Unstructured Nodal Discontinuous Galerkin Method for Convection-Diffusion Equations Applied to Neutral Fluids and Plasmas
… method has been successfully applied to solving hyperbolic conservation laws. Due to its compactness, high order accuracy, and versatility, the DG method has been extensively applied to convection-diffusion problems. In this dissertation, a numerical package, texttt{PHORCE}, is introduced to …
-
Fast Sweeping Methods for Steady State Hyperbolic Conservation Problems and Numerical Applications for Shape Optimization and Computational Cell Biology
… develop a numerical solver for steady states of hyperbolic conservation problems with high order of accuracy and the capability to resolve shocks. Fast sweeping methods are efficient iterative numerical schemes originally designed for solving stationary Hamilton-Jacobi equations. Their efficiency …
-
Speeding up high-order algorithms in computational fluid and kinetic dynamics: based on characteristics tracing and low-rank structures
… third, satisfying physical properties such as conservation, equilibrium preservation and relative entropy dissipation is desired at the discrete level to avoid nonphysical behaviors. The goal of this dissertation is to develop efficient and robust algorithms for solving high-dimensional PDEs in …
-
Adjoint-based optimization for hyperbolic balance laws in the presence of discontinuities
… main discontinuous wave patterns that appear in hyperbolic balance laws: contact discontinuities and shocks. These two have very different characteristics in the forward problem and we will see that they require different treatments for the adjoint formulations as well. Specifically, shocks …