SummationByParts/multigrid/examples/expressions_vortex.json

{
    "grids": {
        "grid": {
            "x": { "linspace": { "start": -5, "end": 5, "steps": 100 } },
            "y": { "linspace": { "start": -5, "end": 5, "steps": 100 } },
            "boundary_conditions": {
                "south": "this",
                "north": "this",
                "east": "this",
                "west": "this"
            },
            "operators": {
                "xi": "upwind9",
                "eta": "upwind9"
            }
        }
    },

    "initial_conditions": {
        "expressions": {
            "globals": "uinf=1;vinf=1;beta=5;y00=0;x00=0;Tfactor=(GAMMA-1)*beta*beta/(8*GAMMA*PI*PI)",
            "rho": "x0=x00+uinf*t;y0=y00+vinf*t; math::pow(1 - Tfactor*math::exp(1 - ((x-x0)*(x-x0) + (y-y0)*(y-y0))), 1.0/(GAMMA - 1))",
            "u": "x0=x00+uinf*t;y0=y00+vinf*t; uinf + beta/(2*PI) * math::exp((1 - ((x-x0)*(x-x0) + (y-y0)*(y-y0)))/2)*(-(y-y0))",
            "v": "x0=x00+uinf*t;y0=y00+vinf*t; vinf + beta/(2*PI) * math::exp((1 - ((x-x0)*(x-x0) + (y-y0)*(y-y0)))/2)*((x-x0))",
            "p": "math::pow(rho, GAMMA)"
        }
    },
    "integration_time": 2.0
}