CAA Using 3D CESE Method with a Simplified Courant Number Insensitive Scheme

Other Applications

“…A 3D simulation was performed for the propagation of a Gaussian acoustic pulse and a vorticity wave embedded in a Mach 0.5 mean flow. Once again, the CESE results were in good agreement with the corresponding analytical solution in preserving both the form and amplitude of the waves [17]. Yen [18] further conducted a series of 3D CESE simulations for the Helmholtz resonator problem.…”

“…Additionally, the authors also pointed out that the non-reflecting boundary condition, which plays an important role in CAA, is much simpler to implement in the CESE method than in traditional methods (see [15,16]). To deal with practical multi-dimensional CAA problems where large disparity in grid cell size is inevitable, Yen et al [17,18] modified the Courant number insensitive (CNI)-CESE scheme [17] and the local time-stepping CESE scheme [18] to improve the numerical efficiency. A 3D simulation was performed for the propagation of a Gaussian acoustic pulse and a vorticity wave embedded in a Mach 0.5 mean flow.…”

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

“…The local CFL ν at the solution point Q * is defined to be the maximum value among ν 1 , ν 2 , ν 3 , ν 4 , ν 5 , ν 6 , ν 7 , and ν 8 . It should be pointed out that as with done to the tetrahedron grid by Yen et al (2006), we calculate the simplified grid CFL for only half time step marching instead of the formal grid CFL for a full Δt in order not to avoid incurring extra mesh management effort. The formal grid CFL for a full Δt involves the influencing cells for a solution point larger than the immediate neighboring cells, and the resulting grid CFL calculation is expensive and complex to apply for our large-scale parallel computation application of solar wind modeling with composite six-component grids.…”

“…For calculating the local CFL number ν, we use a simplified 3D grid CFL calculation as proposed by Yen et al (2006). The simplified 3D grid CFL, according to Yen et al (2006), is defined by enforcing the necessary condition of stability, namely, to require the analytical domain of dependence to be bounded by the numerical domain of dependence, associated with a solution point.…”

“…The simplified 3D grid CFL, according to Yen et al (2006), is defined by enforcing the necessary condition of stability, namely, to require the analytical domain of dependence to be bounded by the numerical domain of dependence, associated with a solution point. Here, both domains of dependence are defined as follows: the numerical domain of dependence (Figure 3 ), is a sphere with a radius of V f Δt/2 (V f is the local speed of fast magnetosonic wave at Q * ) and with a center at point P that is displaced by (−uΔt/2, −vΔt/2, −wΔt/2) from point Q * .…”