Coupled Numerical Methods to Analyze Interacting Acoustic-Dynamic Models by Multidomain Decomposition Techniques

Table 1

ExDCA-1 algorithm.

Time-step loop (based on 𝑡𝑝)
(1) Acoustic subdomains analyses: evaluation of 𝐏^𝑡𝑝.
(2) Subcycling (until 𝑡𝑢=𝑡𝑝):
(2.1) pressure temporal interpolation: 𝐏^𝑡𝑢=∑^𝐽𝑢𝑗=0𝛽𝑗𝐏^(𝑡−𝑗Δ𝑡)𝑝,
(2.2) force-pressure compatibility (spatial interpolation): 𝐅^𝑡𝑢=𝑁𝑢(𝐏^𝑡𝑢),
(2.3) dynamic subdomains analyses: evaluation of 𝐔^𝑡𝑢,
(2.4) evaluation of time derivatives of 𝐔^𝑡𝑢: 𝐔̇^𝑡𝑢 (if necessary), 𝐔̈^𝑡𝑢.
(3) Flux-acceleration compatibility (spatial interpolation): 𝐐^𝑡𝑝=𝑁𝑝(𝐔̈^𝑡𝑝).
(4) Evaluation of time derivatives of 𝐏^𝑡𝑝: 𝐏̇^𝑡𝑝, 𝐏̈^𝑡𝑝 (if necessary).