Modeling 3D Magma Dynamics Using a Discontin- uous Galerkin Method
نویسندگان
چکیده
Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library deal.II . The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance and one elliptic equation to recover global pressure. A combination of a discontinuous Galerkin method for the advection equations and a finite element method for the elliptic equation provide a robust and efficient solution to the channel regime problems of the physical system in 3D. A projective and adaptively applied pressure estimation is employed to significantly reduce the computational wall time without impacting the overall physical reliability in the modeling of important features of melt and segregation, such as melt channel bifurcation in 2D and 3D time dependent simulations. AMS subject classifications: 65Z05, 65M22, 65M60
منابع مشابه
The development of discontinuous
In this paper, we present an overview of the evolution of the discontin-uous Galerkin methods since their introduction in 1973 by Reed and Hill, in the framework of neutron transport, until their most recent developments. We show how these methods made their way into the main stream of computational uid dynamics and how they are quickly nding use in a wide variety of applications. We review the...
متن کاملDispersion analysis of CGM &
The dispersion relation of the semi-discrete continuous and discontin-uous Galerkin formulations are analysed for the linear advection equation. In the context of an spectral/hp element discretisation on an equispaced mesh the problem can be reduced to a P P eigenvalue problem where P is the polynomial order. The analytical dispersion relationships for polynomial order up to P = 3 and the numer...
متن کاملMultilevel and Local Time-stepping Discontinuous Galerkin Methods for Magma Dynamics
Discontinuous Galerkin (DG) method is presented for numerical modeling of melt migration in a chemically reactive and viscously deforming upwelling mantle column at local chemical equilibrium. DG methods for both advection and elliptic equations provide a robust and efficient solution to the problems of melt migration in the asthenospheric upper mantle. Assembling and solving the elliptic equat...
متن کامل3D Finite element modeling for Dynamic Behavior Evaluation of Marin Risers Due to VIV and Internal Flow
The complete 3D nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. For describing the dynamics of the system, the Newtonian derivation procedure is followed. The velocity field inside the pipe formulated using hydrostatic and Bernoulli equations. The hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...
متن کاملOptimization of Meshless Local Petrov-Galerkin Parameters using Genetic Algorithm for 3D Elasto-static Problems (TECHNICAL NOTE)
A truly Meshless Local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-static problems. Using the general MLPG concept, this method is derived through the local weak forms of the equilibrium equations, by using a test function, namely, the Heaviside step function. The Moving Least Squares (MLS) are chosen to construct the shape functions. The penalty approach is used to impose ...
متن کامل