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Introduction to MHD Numerical Simulation in Space
-- Yongli Wang --
for
ESS265: Instrumentation, Data Processing
and
Data Analysis in Space Physics
Professor C. T. Russell
March 25, 1999
UCLA
Contents
Definition of Numerical Simulation
Simulation
Numerical simulation
The Relationship Between Observation, Theoretical Study And Numerical Simulation
Observation
Theoretical study
Numerical simulation
Two Basic Types of Space Numerical Simulation
Particle simulation
MHD(Magnetohydrodynamics) simulation
Components of MHD Numerical Simulation
Normalization of MHD equations
Equations
Non-conservative equations
Full conservative equations
Gas dynamic conservative equations
Time and space discretization and variable arrangement
Time and space discretization
Variable arrangement
Numerical differentiation
Errors
Diffusive error
Fluctuation error
Boundary condition
Fixed boundary condition
Linear boundary condition
Symmetric boundary condition
Time varying boundary condition
Special boundary condition
Initial conditions
Time step
Computation scheme
A Practical Example: One-Dimensional Shock-Tube Problem
Definition of problem
Physical problem
Mathematical problem
Boundary condition
Initial condition
Time and space discretization and variable arrangement
Computation scheme
Naive scheme
First order scheme: Rusanov scheme
Second order scheme: Lax-Wendroff scheme
Conclusion
Further Reading
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