- Title Information
- Title
- Advances in the Discontinuous Galerkin Method: Hybrid Schemes and Applications to the Reactive Infiltration Instability in an Upwelling Compacting Mantle
- Name:
Personal
- Name Part
- Schiemenz, Alan R.
- Role
- Role Term:
Text
- creator
- Origin Information
- Copyright Date
(keyDate="yes", encoding="w3cdtf")
- 2009
- Physical Description
- Extent
- xvii, 120 p.
- digitalOrigin
- born digital
- Note
- Thesis (Ph.D.) -- Brown University (2009)
- Name:
Personal
- Name Part
- Hesthaven, Jan
- Role
- Role Term:
Text
- director
- Name:
Personal
- Name Part
- Shu, Chi-Wang
- Role
- Role Term:
Text
- reader
- Name:
Personal
- Name Part
- Parmentier, Edgar
- Role
- Role Term:
Text
- reader
- Name:
Corporate
- Name Part
- Brown University. Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Genre (aat)
- theses
- Abstract
- High-order methods are emerging in the scientific computing community as superior alternatives to the classical finite difference, finite volume, and continuous finite element
methods. The discontinuous Galerkin (DG) method in particular combines many of the positive features of all of these methods. This thesis presents two projects involving the DG method. First, a
Hybrid scheme is presented, which implements DG areas where the solution is considered smooth, while dropping the order of the scheme elsewhere and implementing a finite volume scheme with
high-order, non-oscillatory solution reconstructions suitable for unstructured mesh. Two such reconstructions from the ENO class are considered in the Hybrid. Successful numerical results are
presented for nonlinear systems of conservation laws in one dimension. Second, the high-order discontinuous Galerkin and Fourier spectral methods are applied to an application modeling
three-phase fluid flow through a porous medium, undergoing solid-fluid reaction due to the reactive infiltration instability (RII). This model incorporates a solid upwelling term and an equation
to track the abundance of the reacting mineral orthopyroxene (opx). After validating the numerical discretization, results are given that provide new insight into the formation of melt channels
in the Earth's mantle. Mantle heterogeneities are observed to be one catalyst for the development of melt channels, and the dissolution of opx produces interesting bifurcations in the melt
channels. An alternative formulation is considered where the mass transfer rate relative to velocity is taken to be infinitely large. In this setting, the stiffest terms are removed, greatly
reducing the cost of time integration.
- Subject (Local)
- Topic
- discontinuous Galerkin method
- Subject (Local)
- Topic
- high-order methods
- Subject (Local)
- Topic
- Reactive Infilitration Instability
- Subject (Local)
- Topic
- Hybrid schemes
- Subject (Local)
- Topic
- finite volume methods
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20091218
- Language
- Language Term:
Code (ISO639-2B)
- eng
- Language Term:
Text
- English
- Identifier:
DOI
- 10.7301/Z0T151X8
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.
- Type of Resource (primo)
- dissertations