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Abstract
Although fluid flows are commonplace, we still have not found a way to simulate them accurately. One example is cyclone forecasting. If we can determine the accurate location of a cyclone’s centre at every instant, we can forecast the path of the cyclone accurately. The NavierStokes (NS) equations model fluid flows accurately, based on various demonstrations performed during the past 150 years. However, the analytical solutions of the NS equations are not yet available (it is one of the seven millennium mathematical problems). We currently calculate the numerical solutions of the NS equations using computers. A limitation of using computers is that we can only perform finite operations. However, there are infinite points in a domain of interest. Therefore, there are two main parts involved in computing accurate numerical solutions of a mathematical model:
1. Selection of the finite points in a domain that provide sufficient information about the characteristics of flows in that domain.
2. Computing accurate velocity fields of the flows at the selected finite points.
The selection of the finite points is normally completed by specialised software. Since we do not know the details of a flow when selecting the points, the selection only reflects the characteristics of the geometry of the domain. The characteristics of velocity fields are hidden in the fields themselves. Therefore, if we want to include the characteristics of a velocity field in selecting the points, we must select the points based on the information from both the geometry of the domain and the velocity field.
In this talk, I will briefly introduce methods I proposed about selecting the finite points and where these methods can be applied to solve practical problems.
1. Selection of the finite points in a domain that provide sufficient information about the characteristics of flows in that domain.
2. Computing accurate velocity fields of the flows at the selected finite points.
The selection of the finite points is normally completed by specialised software. Since we do not know the details of a flow when selecting the points, the selection only reflects the characteristics of the geometry of the domain. The characteristics of velocity fields are hidden in the fields themselves. Therefore, if we want to include the characteristics of a velocity field in selecting the points, we must select the points based on the information from both the geometry of the domain and the velocity field.
In this talk, I will briefly introduce methods I proposed about selecting the finite points and where these methods can be applied to solve practical problems.
Original language  English 

Pages  26 
Number of pages  1 
Publication status  Published  27 Nov 2020 
Event  Research for a Changing World: ILWS Online Conference 2020  Online Duration: 26 Nov 2020 → 27 Nov 2020 https://news.csu.edu.au/latestnews/researchforachangingworldanonlineconference https://www.csu.edu.au/research/ilws/engagement/events/ilwsconference2020 (program and abstracts) 
Conference
Conference  Research for a Changing World 

Period  26/11/20 → 27/11/20 
Other  The Institute’s firstever online conference has been hailed as a “resounding success.” The free conference, which was held November 26 and 27, 2020, was an opportunity for members to share the results and conclusions from recent projects and activities and to showcase the work of our strong research teams. The presentations represented all categories of Institute membership – Full Member, Associate Member, Adjunct and Student. There were also two presentations by undergraduate students associated with the Institute. The Conference is free and open to everyone. The program reflects the multi and transdisciplinary research ethos of ILWS. 
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Dive into the research topics of 'Reliable and accurate computations for fluid flows'. Together they form a unique fingerprint.Activities
 14 Peer review responsibility, including review panel or committee

International Journal for Numerical Methods in Fluids (Journal)
Jan Li (Reviewer)
01 Jun 2022 → 30 Jul 2022Activity: Publication peerreview and editorial work › Peer review responsibility, including review panel or committee

International Journal of Computer Mathematics (Journal)
Zhenquan Li (Reviewer)
01 Aug 2022 → 01 Dec 2022Activity: Publication peerreview and editorial work › Peer review responsibility, including review panel or committee

Numerical Heat Transfer Part B: Fundamentals (Journal)
Jan Li (Reviewer)
18 Aug 2022 → 18 Oct 2022Activity: Publication peerreview and editorial work › Peer review responsibility, including review panel or committee