Okay, thank you very muchvanhees71 said:A very nice book on hydro is Landau and Lifshitz vol. 6.
The Navier-Stokes equations inherently account for variable velocity fields. These equations describe the motion of fluid substances and include terms for velocity, pressure, density, and viscosity. By solving these equations with appropriate boundary and initial conditions, you can model how the velocity of the fluid changes over time and space.
Several numerical methods can be used to solve fluid flow problems with variable velocity, including Finite Difference Methods (FDM), Finite Element Methods (FEM), and Finite Volume Methods (FVM). Each method has its own advantages and is chosen based on the specific requirements of the problem, such as the geometry of the domain and the type of boundary conditions.
Boundary conditions are crucial for accurately simulating fluid flow with variable velocity. Common types include Dirichlet boundary conditions (specifying the velocity at the boundary), Neumann boundary conditions (specifying the gradient of velocity), and mixed boundary conditions. The choice depends on the physical situation being modeled, such as inflow/outflow conditions, no-slip conditions at solid boundaries, or free-slip conditions.
Validation can be done by comparing the simulation results with experimental data or analytical solutions, if available. Benchmark problems with known solutions are often used for this purpose. Additionally, sensitivity analysis and grid independence studies can help ensure that the numerical solution is accurate and reliable.
Common challenges include dealing with complex geometries, ensuring numerical stability and convergence, handling turbulence, and managing computational resources. High Reynolds number flows, which are common in practical applications, often require fine meshes and advanced turbulence models, adding to the computational complexity.