I've tried to simulate fluid dynamics via the N-SE in the past, but they're quite unstable exception for under certain nice conditions. I wonder if we'll cover this type of more physics-y stuff later in the course.
carolyn-wang
How are the pressure and velocity fields in the Navier-Stokes equations are related? Are there ways to make these questions easier to solve given their nonlinearity and the boundary conditions?
agao25
@carolyn-wang I think the velocity and pressure fields are related using Bernoulli's equation which can obtain the pressure from the velocity at a point. In terms of scalars, we're actually solving for 3 separate NSEs because x, y, and z might have different constraints or conditions. In ME 106, one thing that made the equations possible to solve by hand is by using assumptions like inviscid, incompressible, laminar, 2D flow. These assumptions allowed us to zero out terms in the equations, but without them, our computers are trying to solve these multidimensional partial differential equations which is a massive computational load.
Rogeryu1234
As a physics major, it is so fansicating to see such fluid dynamic concept in this class! I can still remember my mechanics professor talked about this equation in his office hour and this nonlinear PDE is very hard to solve, I am glad that we learned a way to solve this
I've tried to simulate fluid dynamics via the N-SE in the past, but they're quite unstable exception for under certain nice conditions. I wonder if we'll cover this type of more physics-y stuff later in the course.
How are the pressure and velocity fields in the Navier-Stokes equations are related? Are there ways to make these questions easier to solve given their nonlinearity and the boundary conditions?
@carolyn-wang I think the velocity and pressure fields are related using Bernoulli's equation which can obtain the pressure from the velocity at a point. In terms of scalars, we're actually solving for 3 separate NSEs because x, y, and z might have different constraints or conditions. In ME 106, one thing that made the equations possible to solve by hand is by using assumptions like inviscid, incompressible, laminar, 2D flow. These assumptions allowed us to zero out terms in the equations, but without them, our computers are trying to solve these multidimensional partial differential equations which is a massive computational load.
As a physics major, it is so fansicating to see such fluid dynamic concept in this class! I can still remember my mechanics professor talked about this equation in his office hour and this nonlinear PDE is very hard to solve, I am glad that we learned a way to solve this