SummationByParts/multigrid/examples/gresho.json

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{
"grids": {
"grid": {
"operators": {
"xi": "upwind9",
"eta": "upwind9"
},
"x": { "linspace": { "start": -1, "end": 1, "steps": 200 } },
"y": { "linspace": { "start": -1, "end": 1, "steps": 200 } },
"boundary_conditions": {
"east": "this",
"west": "this",
"north": "this",
"south": "this"
}
}
},
"integration_time": 2.0,
"initial_conditions": {
"expressions": {
"globals": "Mach = 0.4; p0 = 1/(GAMMA * Mach^2);",
"rho": "1",
"u": "r=math::hypot(x,y); -math::sin(math::atan2(y, x)) * case(r < 0.2, 5*r, r < 0.4, 2 - 5*r, 0)",
"v": "r=math::hypot(x,y); math::cos(math::atan2(y, x)) * case(r < 0.2, 5*r, r < 0.4, 2 - 5*r, 0)",
"p": "r=math::hypot(x,y); case(r < 0.2, p0 + 25.0/2.0*r*r, r < 0.4, p0 + 25.0/2.0*r*r + 4*(1 - 5*r - math::ln(0.2) + math::ln(r)), p0 - 2 + 4*math::ln(2))"
}
},
"gamma": 1.66666666667
}