Temporal discretization
Mathematical technique / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Temporal discretization?
Summarize this article for a 10 year old
In applied physics and engineering, temporal discretization is a mathematical technique for solving transient problems, such as flow problems.
This article may be too technical for most readers to understand. (May 2014) |
Transient problems are often solved using computer-aided engineering (CAE) simulations, which require discretizing the governing equations in both space and time. Temporal discretization involves the integration of every term in various equations over a time step ().
The spatial domain can be discretized to produce a semi-discrete form:[1]
The first-order temporal discretization using backward differences is [2]
And the second-order discretization is
where
- is a scalar
- is the value at the next time,
- is the value at the current time,
- is the value at the previous time,
The function is evaluated using implicit- and explicit-time integration.[3]