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1. |
Consider the stencil. Assume a uniform grid. What is \(\dot{m_w} \phi_{wv}\) according to the second-order upwind scheme?(Note: \(\dot{m}\) and φ are the mass flow rate and flow variable). |
A. | \(\dot{m_w}\phi_w=(\frac{3}{2}\phi_P-\frac{1}{2}\phi_W)max(\dot{m_w},0)+(\frac{3}{2}\phi_W-\frac{1}{2}\phi_{WW}) max(-\dot{m_w},0)\) |
B. | \(\dot{m_w}\phi_w=(\frac{3}{2}\phi_P-\frac{1}{2}\phi_W)max(\dot{m_w},0)-(\frac{3}{2}\phi_W-\frac{1}{2}\phi_{WW}) max(-\dot{m_w},0)\) |
C. | \(\dot{m_w}\phi_w=(\frac{3}{2}\phi_P-\frac{1}{2}\phi_W)max(-\dot{m_w},0)+(\frac{3}{2}\phi_W-\frac{1}{2}\phi_{WW}) max(-\dot{m_w},0)\) |
D. | \(\dot{m_w}\phi_w=(\frac{3}{2}\phi_P-\frac{1}{2}\phi_W)max(-\dot{m_w},0)-(\frac{3}{2}\phi_W-\frac{1}{2}\phi_{WW}) max(-\dot{m_w},0)\) |
E. | .a) \(\dot{m_w}\phi_w=(\frac{3}{2}\phi_P-\frac{1}{2}\phi_W)max(\dot{m_w},0)+(\frac{3}{2}\phi_W-\frac{1}{2}\phi_{WW}) max(-\dot{m_w},0)\) b) \(\dot{m_w}\phi_w=(\frac{3}{2}\phi_P-\frac{1}{2}\phi_W)max(\dot{m_w},0)-(\frac{3}{2}\phi_W-\frac{1}{2}\phi_{WW}) max(-\dot{m_w},0)\) c) \(\dot{m_w}\phi_w=(\frac{3}{2}\phi_P-\frac{1}{2}\phi_W)max(-\dot{m_w},0)+(\frac{3}{2}\phi_W-\frac{1}{2}\phi_{WW}) max(-\dot{m_w},0)\) d) \(\dot{m_w}\phi_w=(\frac{3}{2}\phi_P-\frac{1}{2}\phi_W)max(-\dot{m_w},0)-(\frac{3}{2}\phi_W-\frac{1}{2}\phi_{WW}) max(-\dot{m_w},0)\) |
Answer» C. \(\dot{m_w}\phi_w=(\frac{3}{2}\phi_P-\frac{1}{2}\phi_W)max(-\dot{m_w},0)+(\frac{3}{2}\phi_W-\frac{1}{2}\phi_{WW}) max(-\dot{m_w},0)\) | |