Benchmarks

An Introduction and Tutorial to the "McKenzie Equations" for Magma Migration — by Sue Kientz — last modified 2007-01-15 01:43 PM

A new formulation for the equations of magma migration in viscous materials as originally derived by McKenzie is presented, as well as a set of well-understood special case problems that form a useful benchmark-suite for developing and testing new codes.

Running stgMADDs Benchmarks — by Sue Kientz — last modified 2008-02-08 02:09 AM

The Magma Development team has finished the alpha release of the Magma Dynamics Demonstration Suite (MADDs). The initial code implements the zero porosity/no melting magma benchmark for mid-ocean ridge solid flows in 2D and 3D built on the Underworld framework. The purpose of this code is principally to validate accurate pressure solvers for Stokes flow in current CIG supported software. The stgMADDs source code is available in CIG's Mercurial Repository (geodynamics.org/hg).

Milestone 1 Results and Analysis — by Dave Lee — last modified 2008-02-08 02:14 AM

Details how to run the first milestone of the MADDs project in 2D and 3D and provides some results of these simulations. It also gives the rates of convergence of the pressure gradient solutions as the resolution is increased.

2D Ridge Model — by Dave Lee — last modified 2008-02-08 02:26 AM

Velocity, pressure and pressure gradients solutions and L2 errors for a 2D ridge model with 120 x 60 elements.

3D Ridge Model — by Dave Lee — last modified 2008-02-08 02:26 AM

Velocity, pressure and pressure gradient solutions and L2 error fields for 3D ridge model.

Global Pressure Gradient Errors for 2D Ridge Model — by Dave Lee — last modified 2008-02-08 02:28 AM

Normalised global L2 errors.

Global Pressure Gradient Errors for 3D Ridge Model — by Dave Lee — last modified 2008-02-08 02:28 AM

Global normalised L2 pressure gradient errors at varying resolutions.

Milestone 2 Results and Analysis — by Dave Lee — last modified 2008-02-08 03:04 AM

Details the results of the Milestone 2 simulations and analyzes the accuracy of the advection scheme.

Gaussian Porosity Field Advection — by Dave Lee — last modified 2008-02-08 02:25 AM

Advection of Gaussian porosity field as a Stokes equation force term. The lower density porosity region rises due to gravity.

Ridge Model with Gaussian Porosity Field — by Dave Lee — last modified 2008-02-08 02:26 AM

Stokes flow with 2D ridge model boundary conditions and Gaussian porosity initial distribution, driven by a porosity dependent force term.

Semi Lagrangian Advection Scheme Test - Step Function — by Dave Lee — last modified 2008-02-08 02:39 AM

Diagonal step function initial distribution subjected to a shearing velocity field.

Semi Lagrangian Advection Scheme Test - Gaussian Distribution — by Dave Lee — last modified 2008-02-08 02:42 AM

Gaussian initial distribution subjected to a shearing velocity field.

Error Convergence for Advection Scheme - Step Function IC — by Dave Lee — last modified 2008-02-08 02:44 AM

Normalised global L2 errors for semi Lagrangian advection scheme with a diagonal step function initial condition as a function of resolution.

Error Convergence for Advection Scheme - Gaussian IC — by Dave Lee — last modified 2008-02-08 02:46 AM

Normalised global L2 errors for semi Lagrangian advection scheme with Gaussian initial distribution as a function of resolution.

Milestone 3 Results — by Dave Lee — last modified 2008-02-08 02:52 AM

Details the results for the third milestone, in which the melt velocity was determined given the existing solid velocity and pressure fields.

Melt Model - 2D Ridge with Constant Porosity — by Dave Lee — last modified 2008-02-08 02:55 AM

Solid and melt velocity, pressure and pressure gradient fields for 2D ridge model with constant porosity. Melt velocity magnitudes are significantly larger near the point of discontinuity due to their proportionality to the pressure gradients, which are largest at these points.

Melt Model - Gaussian Porosity Driven Flow — by Dave Lee — last modified 2008-02-08 02:57 AM

Solid and melt velocity, pressure and pressure gradient fields for Stokes flow driven by a Gaussian initial porosity distribution.

Milestone 4 Results and Analysis — by Dave Lee — last modified 2008-09-28 11:16 AM

Discussion of the system being modeled, and details of how to run the model with different initial conditions in 2 and 3D.

2D Solitary Wave — by Dave Lee — last modified 2008-05-18 02:32 PM

A 2D solitary wave with a wave speed of 7 rising through a solid with a constant speed of -2. The wave shows no visible diffusive behavior.

Noisy 1D Solitary Wave Initial Condition — by Dave Lee — last modified 2008-05-18 02:38 PM

Initial condition of a vertically changing 1D solitary wave with a certain amount of introduced noise, which allows 2D solitary waves to emerge over time.

Emerging 2D Solitary Waves — by Dave Lee — last modified 2008-05-18 02:41 PM

Solitary waves emerging from a noisy 1D solitary wave initial condition.

Emergent 2D Solitary Waves — by Dave Lee — last modified 2008-05-18 02:47 PM

Solitary waves having emerged from a noisy 1D solitary wave initial distribution.

Emergent 3D Solitary Waves. — by Dave Lee — last modified 2008-09-28 10:41 AM

3D Solitary Waves emerging from a noisy 1D Solitary Wave initial distribution

Milestone 5 Results and Analysis — by Dave Lee — last modified 2008-09-28 11:30 AM

Results and analysis for the isoviscous McKenzie equations (with melting) driven by a corner flow velocity BC.

Isoviscous McKenzie System with Corner Flow BC - 1 — by Dave Lee — last modified 2008-09-28 11:03 AM

After 1 time step

Isoviscous McKenzie System with Corner Flow BC - 50 — by Dave Lee — last modified 2008-09-28 11:05 AM

After 50 time steps