What are the Functions of Riemann Invariants?

Thread starter lavster
Start date Oct 24, 2010
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Invariant Riemann

In summary, Riemann Invariants are a mathematical concept used in fluid dynamics to describe the behavior of a fluid flow. They remain constant along a fluid path and are important in simplifying the equations that govern fluid flow. Riemann Invariants are closely related to conservation laws and can be applied to all types of fluid flow. They are calculated using the Euler equations.

Oct 24, 2010

lavster

Can someone tell me what a riemann invariant is in general terms please? i can't find it anywhere!

thanks, lav

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Oct 24, 2010

slider142

This book came up immediately in a Google search. They are functions of various contractions of the Riemann tensor.

Related to What are the Functions of Riemann Invariants?

1. What is the definition of a Riemann Invariant?

A Riemann Invariant is a mathematical concept used in fluid dynamics to describe the behavior of a fluid flow. It is a quantity that remains constant along a fluid path, even as the properties of the fluid may change.

2. What is the significance of Riemann Invariants in fluid dynamics?

Riemann Invariants are important in fluid dynamics because they allow us to simplify the equations that govern fluid flow. By using these invariants, we can reduce complex equations to simpler forms, making it easier to analyze and understand the behavior of fluids.

3. How are Riemann Invariants related to conservation laws?

Riemann Invariants are closely related to conservation laws, specifically the conservation of mass, momentum, and energy. In fact, Riemann Invariants arise from these laws and are used to express them in a more convenient form.

4. Can Riemann Invariants be applied to all types of fluid flow?

Yes, Riemann Invariants can be applied to all types of fluid flow, including compressible and incompressible flows. However, different forms of Riemann Invariants may be used for different types of flows.

5. How are Riemann Invariants calculated?

Riemann Invariants are calculated using the equations of fluid dynamics, specifically the Euler equations. These equations can be solved to find the Riemann Invariants at any point along a fluid path.