Completely conservative difference schemes for two-dimensional magnetohydrodynamic equations

1974 ◽  
Vol 14 (3) ◽  
pp. 257-262
Author(s):  
N.V. Belan ◽  
N.A. Mashtylev ◽  
L.V. Shushlyapin
Keyword(s):  
Difference Schemes ◽  
Two Dimensional ◽  
Magnetohydrodynamic Equations ◽  
Conservative Difference Schemes ◽  
Conservative Difference

Numerische Simulation von Diffusionsprozessen mit nichtnegativitätserhaltenden konservativen Differenzenverfahren /

1982 ◽  
Vol 37 (8) ◽  
Author(s):  
Rudolf Gorenflo ◽  
Angelika Kuban
Keyword(s):  
Heat Equation ◽  
Linear Equation ◽  
Source Term ◽  
Difference Schemes ◽  
General Linear ◽  
Two Dimensional ◽  
Numerische Simulation ◽  
General Linear Equation ◽  
Conservative Difference Schemes ◽  
Conservative Difference

After analyzing the general linear equation of diffusion (of a substance or of energy) with source term and given influx across the boundary we describe a method for constructing explicit and implicit conservative difference schemes which also preserve nonnegativity. We call a scheme “conservative” if via a convenient sum-analogue it does exactly imitate the conservation of a substance or energy. We concretize this method for the spatially two-dimensional heat equation in a rectangle with given influx. We also present a conservative implicit scheme with alternating directions

Numerische Simulation von Diffusionsprozessen mit nichtnegativitätserhaltenden konservativen Differenzenverfahren / Numerical Simulation of Diffusion Processes with conservative difference schemes of non-negative type

1982 ◽  
Vol 37 (8) ◽  
pp. 759-768 ◽  
Author(s):  
Rudolf Gorenflo ◽  
Angelika Kuban
Keyword(s):  
Numerical Simulation ◽  
Heat Equation ◽  
Source Term ◽  
Diffusion Processes ◽  
Difference Schemes ◽  
Two Dimensional ◽  
Numerische Simulation ◽  
General Linear Equation ◽  
Conservative Difference Schemes ◽  
Conservative Difference

After analyzing the general linear equation of diffusion (of a substance or of energy) with source term and given influx across the boundary we describe a method for constructing explicit and implicit conservative difference schemes which also preserve nonnegativity. We call a scheme “conservative” if via a convenient sum-analogue it does exactly imitate the conservation of a substance or energy. We concretize this method for the spatially two-dimensional heat equation in a rectangle with given influx. We also present a conservative implicit scheme with alternating directions

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