Week 9 - FVM Literature Review

A comprehensive survey on the Finite Volume Method (FVM) in Computational Fluid Dynamics (CFD) can delve into various aspects of the technique, its applications, and advancements. Here is a concise outline of what a literature review on FVM in CFD could encompass:

Introduction to FVM:

1. Definition and Fundamental Principles of FVM:

   • Explanation of FVM's core concepts and principles.
   • Comparison with other numerical methods employed in CFD, such as Finite Difference Method (FDM) and Finite Element Method (FEM).
   • Discussion of the advantages and limitations associated with FVM.

2. Numerical Formulation of FVM:

   • Discretization of governing equations using FVM.
   • Overview of control volumes and the application of conservation laws.
   • Treatment of boundary conditions within the FVM framework.

3. FVM Computations and Solvers:

   • Overview of various algorithms utilized in FVM, including explicit, implicit, and semi-implicit schemes.
   • Explanation of linear and nonlinear solvers integrated into FVM.
   • Introduction to time integration methods commonly employed with FVM.

4. Applications of FVM:

   • Overview of prominent application areas where FVM finds extensive use, such as aerodynamics, heat transfer, multiphase flows, combustion, and turbomachinery.
   • Detailed examples showcasing FVM applications in specific engineering problems or industrial sectors.
   • Comparison of FVM with other numerical methods in terms of accuracy, efficiency, and suitability for diverse problems.

5. Advanced Techniques and Recent Developments:

   • High-order accurate schemes for FVM, including MUSCL (Monotonic Upstream-Centered Schemes for Conservation Laws) and WENO (Weighted Essentially Non-Oscillatory) schemes.
   • Employment of adaptive grid methods and mesh refinement strategies within FVM.
   • Parallel computing and GPU acceleration for simulations based on FVM.
   • Integration of turbulence models into FVM for turbulent flow simulations.
   • Coupling FVM with other computational techniques, such as FEM or immersed boundary methods.

6. Challenges and Future Directions:

   • Identification of existing challenges and limitations of FVM in CFD.
   • Exploration of emerging trends and potential research areas in FVM.

7. Potential Advances in FVM Algorithms, Numerical Schemes, and Computational Techniques.

Conclusion:

• Summarization of key findings and insights gleaned from the reviewed literature.
• Overall assessment of the strengths and weaknesses of FVM in CFD.
• Envisioned future prospects and areas of growth for FVM.

While conducting a literature review, it is crucial to search for relevant research papers, conference proceedings, and authoritative books or review articles in the realm of computational fluid dynamics and numerical methods. This will help build a comprehensive and up-to-date collection of literature to review and analyze.