Questions about boundary TYPE_E

[JohnZhan2023]

I would like to simulate the response of an object in an air fluid. For this, I have set the left side as the inlet, the right side as the outlet, and periodic boundary conditions for the top, bottom, front, and back. The left side has a velocity directed towards the right, while the right side is configured to allow free outflow.

However, I have observed that during the simulation, a backward shock wave appears at the left wall, as though the outflow condition is not functioning as expected. I would greatly appreciate any insights or suggestions as to why this might be occurring.

Here are the detailed settings I have used:

parallel_for(lbm.get_N(), [&](ulong n) {
    uint x=0u, y=0u, z=0u;
    lbm.coordinates(n, x, y, z);

    // Default initial values: rho=1, u=0, flags=0 (inside fluid)
    // Below, modifications will be made as needed
    // (1) Inlet (x=0): Set velocity boundary
    if(x == 0u) {
        lbm.flags[n] = TYPE_E;      // Fluid boundary, use Equilibrium boundary
        lbm.u.x[n]   = U_in;        // Set velocity in the x direction
        lbm.u.y[n]   = 0.0f;
        lbm.u.z[n]   = 0.0f;
    }

    // (2) Outlet (x=Nx-1): Can specify a near free outflow
    //     Method A: Approximate velocity as (U_in, 0, 0), or smaller
    //     Method B: Set density rho != 1
    //     The following demonstrates a simple "velocity" specification
    if(x == Nx_1) {
        lbm.flags[n] = TYPE_E;      // Equilibrium boundary
        // lbm.u.x[n]   = U_in;        // Can also be set to a smaller value, such as 0.8f*U_in
        // lbm.u.y[n]   = 0.0f;
        // lbm.u.z[n]   = 0.0f;
        lbm.rho[n]   = 1.0f;  // Or slightly less than 1.0f to simulate a slight pressure gradient
    }

    // (3) Top, bottom, front, and back boundaries: Rigid walls
    // if(y == 0u || y == Ny_1 || z == 0u || z == Nz_1) {
    //     lbm.flags[n] = TYPE_S;      // No-slip boundary
    //     // set the transparent boundary
    // }
});

[JohnZhan2023]

Also， I want to ask about what the redlines mean?

And what will cause the red lines?

My code is as follows:

// --------------------------- 1. Define Physical Quantities, Grid, and Flow Parameters ---------------------------
// Example: Set Reynolds number Re, characteristic length D (obstacle diameter), and inlet velocity U_in
const float Re       = 4000.0f;   // Example: Reynolds number around 4000
const float D        = 100.0f;    // Cylinder diameter (LBM length unit)
const float U_in     = 0.05f;     // Inlet velocity (LBM velocity unit, typical range ~0.001 - 0.1)
// From Re = (U_in * D) / nu => nu = (U_in * D) / Re
const float nu       = (U_in * D) / Re;

// Define the dimensions of the wind tunnel: assume that the length direction x is much larger, and y, z are the height and width
// This is just an example; you can adjust the size as needed
const float Lx = 10.0f * D;  // Length in the x direction
const float Ly = 2.0f  * D;  // Height in the y direction
const float Lz = 2.0f  * D;  // Width in the z direction

// Convert floating-point dimensions to integer grid sizes
// For example, aiming for ~5-6 million grid cells in total volume Nx*Ny*Nz
// Simple example: 1 cell corresponds to 1 LBM length unit in each direction
const uint Nx = (uint)ceil(Lx);
const uint Ny = (uint)ceil(Ly);
const uint Nz = (uint)ceil(Lz);
float3 axis = axis_ * (Nx, Ny, Nz); //0, 4, 5, 6

// --------------------------- 2. Create LBM Simulation Object ---------------------------
// Here, only a single GPU is used, and no additional body forces are applied (fx=fy=fz=0.0f)
LBM lbm(Nx, Ny, Nz, nu, 0.0f, 0.0f, 0.0f);