16const int DeltaDegree = 6;
18double MMCollisionInt::delta[8] = {0.0, 0.25, 0.50, 0.75, 1.0,
22double quadInterp(
double x0,
double* x,
double* y)
24 double dx21 = x[1] - x[0];
25 double dx32 = x[2] - x[1];
26 double dx31 = dx21 + dx32;
27 double dy32 = y[2] - y[1];
28 double dy21 = y[1] - y[0];
29 double a = (dx21*dy32 - dy21*dx32)/(dx21*dx31*dx32);
30 return a*(x0 - x[0])*(x0 - x[1]) + (dy21/dx21)*(x0 - x[1]) + y[1];
33double MMCollisionInt::tstar22[37] = {
34 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0,
35 1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 3.5, 4.0,
36 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 12.0, 14.0, 16.0,
37 18.0, 20.0, 25.0, 30.0, 35.0, 40.0, 50.0, 75.0, 100.0
41 4.1005, 4.266, 4.833, 5.742, 6.729, 8.624, 10.34, 11.89,
42 3.2626, 3.305, 3.516, 3.914, 4.433, 5.57, 6.637, 7.618,
43 2.8399, 2.836, 2.936, 3.168, 3.511, 4.329, 5.126, 5.874,
44 2.531, 2.522, 2.586, 2.749, 3.004, 3.64, 4.282, 4.895,
45 2.2837, 2.277, 2.329, 2.46, 2.665, 3.187, 3.727, 4.249,
46 2.0838, 2.081, 2.13, 2.243, 2.417, 2.862, 3.329, 3.786,
47 1.922, 1.924, 1.97, 2.072, 2.225, 2.614, 3.028, 3.435,
48 1.7902, 1.795, 1.84, 1.934, 2.07, 2.417, 2.788, 3.156,
49 1.6823, 1.689, 1.733, 1.82, 1.944, 2.258, 2.596, 2.933,
50 1.5929, 1.601, 1.644, 1.725, 1.838, 2.124, 2.435, 2.746,
51 1.4551, 1.465, 1.504, 1.574, 1.67, 1.913, 2.181, 2.451,
52 1.3551, 1.365, 1.4, 1.461, 1.544, 1.754, 1.989, 2.228,
53 1.28, 1.289, 1.321, 1.374, 1.447, 1.63, 1.838, 2.053,
54 1.2219, 1.231, 1.259, 1.306, 1.37, 1.532, 1.718, 1.912,
55 1.1757, 1.184, 1.209, 1.251, 1.307, 1.451, 1.618, 1.795,
56 1.0933, 1.1, 1.119, 1.15, 1.193, 1.304, 1.435, 1.578,
57 1.0388, 1.044, 1.059, 1.083, 1.117, 1.204, 1.31, 1.428,
58 0.99963, 1.004, 1.016, 1.035, 1.062, 1.133, 1.22, 1.319,
59 0.96988, 0.9732, 0.983, 0.9991, 1.021, 1.079, 1.153, 1.236,
60 0.92676, 0.9291, 0.936, 0.9473, 0.9628, 1.005, 1.058, 1.121,
61 0.89616, 0.8979, 0.903, 0.9114, 0.923, 0.9545, 0.9955, 1.044,
62 0.87272, 0.8741, 0.878, 0.8845, 0.8935, 0.9181, 0.9505, 0.9893,
63 0.85379, 0.8549, 0.858, 0.8632, 0.8703, 0.8901, 0.9164, 0.9482,
64 0.83795, 0.8388, 0.8414, 0.8456, 0.8515, 0.8678, 0.8895, 0.916,
65 0.82435, 0.8251, 0.8273, 0.8308, 0.8356, 0.8493, 0.8676, 0.8901,
66 0.80184, 0.8024, 0.8039, 0.8065, 0.8101, 0.8201, 0.8337, 0.8504,
67 0.78363, 0.784, 0.7852, 0.7872, 0.7899, 0.7976, 0.8081, 0.8212,
68 0.76834, 0.7687, 0.7696, 0.7712, 0.7733, 0.7794, 0.7878, 0.7983,
69 0.75518, 0.7554, 0.7562, 0.7575, 0.7592, 0.7642, 0.7711, 0.7797,
70 0.74364, 0.7438, 0.7445, 0.7455, 0.747, 0.7512, 0.7569, 0.7642,
71 0.71982, 0.72, 0.7204, 0.7211, 0.7221, 0.725, 0.7289, 0.7339,
72 0.70097, 0.7011, 0.7014, 0.7019, 0.7026, 0.7047, 0.7076, 0.7112,
73 0.68545, 0.6855, 0.6858, 0.6861, 0.6867, 0.6883, 0.6905, 0.6932,
74 0.67232, 0.6724, 0.6726, 0.6728, 0.6733, 0.6743, 0.6762, 0.6784,
75 0.65099, 0.651, 0.6512, 0.6513, 0.6516, 0.6524, 0.6534, 0.6546,
76 0.61397, 0.6141, 0.6143, 0.6145, 0.6147, 0.6148, 0.6148, 0.6147,
77 0.5887, 0.5889, 0.5894, 0.59, 0.5903, 0.5901, 0.5895, 0.5885
82 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0,
83 1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 3.5, 4.0,
84 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 12.0, 14.0, 16.0,
85 18.0, 20.0, 25.0, 30.0, 35.0, 40.0, 50.0, 75.0, 100.0, 500.0
89 1.0065, 1.0840, 1.0840, 1.0840, 1.0840, 1.0840, 1.0840, 1.0840,
90 1.0231, 1.0660, 1.0380, 1.0400, 1.0430, 1.0500, 1.0520, 1.0510,
91 1.0424, 1.0450, 1.0480, 1.0520, 1.0560, 1.0650, 1.0660, 1.0640,
92 1.0719, 1.0670, 1.0600, 1.0550, 1.0580, 1.0680, 1.0710, 1.0710,
93 1.0936, 1.0870, 1.0770, 1.0690, 1.0680, 1.0750, 1.0780, 1.0780,
94 1.1053, 1.0980, 1.0880, 1.0800, 1.0780, 1.0820, 1.0840, 1.0840,
95 1.1104, 1.1040, 1.0960, 1.0890, 1.0860, 1.0890, 1.0900, 1.0900,
96 1.1114, 1.1070, 1.1000, 1.0950, 1.0930, 1.0950, 1.0960, 1.0950,
97 1.1104, 1.1070, 1.1020, 1.0990, 1.0980, 1.1000, 1.1000, 1.0990,
98 1.1086, 1.1060, 1.1020, 1.1010, 1.1010, 1.1050, 1.1050, 1.1040,
99 1.1063, 1.1040, 1.1030, 1.1030, 1.1040, 1.1080, 1.1090, 1.1080,
100 1.1020, 1.1020, 1.1030, 1.1050, 1.1070, 1.1120, 1.1150, 1.1150,
101 1.0985, 1.0990, 1.1010, 1.1040, 1.1080, 1.1150, 1.1190, 1.1200,
102 1.0960, 1.0960, 1.0990, 1.1030, 1.1080, 1.1160, 1.1210, 1.1240,
103 1.0943, 1.0950, 1.0990, 1.1020, 1.1080, 1.1170, 1.1230, 1.1260,
104 1.0934, 1.0940, 1.0970, 1.1020, 1.1070, 1.1160, 1.1230, 1.1280,
105 1.0926, 1.0940, 1.0970, 1.0990, 1.1050, 1.1150, 1.1230, 1.1300,
106 1.0934, 1.0950, 1.0970, 1.0990, 1.1040, 1.1130, 1.1220, 1.1290,
107 1.0948, 1.0960, 1.0980, 1.1000, 1.1030, 1.1120, 1.1190, 1.1270,
108 1.0965, 1.0970, 1.0990, 1.1010, 1.1040, 1.1100, 1.1180, 1.1260,
109 1.0997, 1.1000, 1.1010, 1.1020, 1.1050, 1.1100, 1.1160, 1.1230,
110 1.1025, 1.1030, 1.1040, 1.1050, 1.1060, 1.1100, 1.1150, 1.1210,
111 1.1050, 1.1050, 1.1060, 1.1070, 1.1080, 1.1110, 1.1150, 1.1200,
112 1.1072, 1.1070, 1.1080, 1.1080, 1.1090, 1.1120, 1.1150, 1.1190,
113 1.1091, 1.1090, 1.1090, 1.1100, 1.1110, 1.1130, 1.1150, 1.1190,
114 1.1107, 1.1110, 1.1110, 1.1110, 1.1120, 1.1140, 1.1160, 1.1190,
115 1.1133, 1.1140, 1.1130, 1.1140, 1.1140, 1.1150, 1.1170, 1.1190,
116 1.1154, 1.1150, 1.1160, 1.1160, 1.1160, 1.1170, 1.1180, 1.1200,
117 1.1172, 1.1170, 1.1170, 1.1180, 1.1180, 1.1180, 1.1190, 1.1200,
118 1.1186, 1.1190, 1.1190, 1.1190, 1.1190, 1.1190, 1.1200, 1.1210,
119 1.1199, 1.1200, 1.1200, 1.1200, 1.1200, 1.1210, 1.1210, 1.1220,
120 1.1223, 1.1220, 1.1220, 1.1220, 1.1220, 1.1230, 1.1230, 1.1240,
121 1.1243, 1.1240, 1.1240, 1.1240, 1.1240, 1.1240, 1.1250, 1.1250,
122 1.1259, 1.1260, 1.1260, 1.1260, 1.1260, 1.1260, 1.1260, 1.1260,
123 1.1273, 1.1270, 1.1270, 1.1270, 1.1270, 1.1270, 1.1270, 1.1280,
124 1.1297, 1.1300, 1.1300, 1.1300, 1.1300, 1.1300, 1.1300, 1.1290,
125 1.1339, 1.1340, 1.1340, 1.1350, 1.1350, 1.1340, 1.1340, 1.1320,
126 1.1364, 1.1370, 1.1370, 1.1380, 1.1390, 1.1380, 1.1370, 1.1350,
127 1.14187, 1.14187, 1.14187, 1.14187, 1.14187, 1.14187, 1.14187,
132 1.1852, 1.2963, 1.2963, 1.2963, 1.2963, 1.2963,1.2963, 1.2963,
133 1.1960, 1.216, 1.237, 1.269, 1.285, 1.290, 1.297, 1.294,
134 1.2451, 1.257, 1.340, 1.389, 1.366, 1.327, 1.314, 1.278,
135 1.2900, 1.294, 1.272, 1.258, 1.262, 1.282, 1.290, 1.299,
136 1.2986, 1.291, 1.284, 1.278, 1.277, 1.288, 1.294, 1.297,
137 1.2865, 1.281, 1.276, 1.272, 1.277, 1.286, 1.292, 1.298,
138 1.2665, 1.264, 1.261, 1.263, 1.269, 1.284, 1.292, 1.298,
139 1.2455, 1.244, 1.248, 1.255, 1.262, 1.278, 1.289, 1.296,
140 1.2253, 1.225, 1.234, 1.240, 1.252, 1.271, 1.284, 1.295,
141 1.2078, 1.210, 1.216, 1.227, 1.242, 1.264, 1.281, 1.292,
142 1.1919, 1.192, 1.205, 1.216, 1.230, 1.256, 1.273, 1.287,
143 1.1678, 1.172, 1.181, 1.195, 1.209, 1.237, 1.261, 1.277,
144 1.1496, 1.155, 1.161, 1.174, 1.189, 1.221, 1.246, 1.266,
145 1.1366, 1.141, 1.147, 1.159, 1.174, 1.202, 1.231, 1.256,
146 1.1270, 1.130, 1.138, 1.148, 1.162, 1.191, 1.218, 1.242,
147 1.1197, 1.122, 1.129, 1.140, 1.149, 1.178, 1.205, 1.231,
148 1.1080, 1.110, 1.116, 1.122, 1.132, 1.154, 1.180, 1.205,
149 1.1016, 1.103, 1.107, 1.112, 1.120, 1.138, 1.160, 1.183,
150 1.0980, 1.099, 1.102, 1.106, 1.112, 1.127, 1.145, 1.165,
151 1.0958, 1.097, 1.099, 1.102, 1.107, 1.119, 1.135, 1.153,
152 1.0935, 1.094, 1.095, 1.097, 1.100, 1.109, 1.120, 1.134,
153 1.0925, 1.092, 1.094, 1.095, 1.098, 1.104, 1.112, 1.122,
154 1.0922, 1.092, 1.093, 1.094, 1.096, 1.100, 1.106, 1.115,
155 1.0922, 1.092, 1.093, 1.093, 1.095, 1.098, 1.103, 1.110,
156 1.0923, 1.092, 1.093, 1.093, 1.094, 1.097, 1.101, 1.106,
157 1.0923, 1.092, 1.092, 1.093, 1.094, 1.096, 1.099, 1.103,
158 1.0927, 1.093, 1.093, 1.093, 1.094, 1.095, 1.098, 1.101,
159 1.0930, 1.093, 1.093, 1.093, 1.094, 1.094, 1.096, 1.099,
160 1.0933, 1.094, 1.093, 1.094, 1.094, 1.095, 1.096, 1.098,
161 1.0937, 1.093, 1.094, 1.094, 1.094, 1.094, 1.096, 1.097,
162 1.0939, 1.094, 1.094, 1.094, 1.094, 1.095, 1.095, 1.097,
163 1.0943, 1.094, 1.094, 1.094, 1.095, 1.095, 1.096, 1.096,
164 1.0944, 1.095, 1.094, 1.094, 1.094, 1.095, 1.095, 1.096,
165 1.0944, 1.094, 1.095, 1.094, 1.094, 1.095, 1.096, 1.096,
166 1.0943, 1.095, 1.094, 1.094, 1.095, 1.095, 1.095, 1.095,
167 1.0941, 1.094, 1.094, 1.094, 1.094, 1.094, 1.094, 1.096,
168 1.0947, 1.095, 1.094, 1.094, 1.093, 1.093, 1.094, 1.095,
169 1.0957, 1.095, 1.094, 1.093, 1.092, 1.093, 1.093, 1.094,
170 1.10185, 1.10185, 1.10185, 1.10185, 1.10185, 1.10185, 1.10185,
175 0.8889, 0.77778, 0.77778,0.77778,0.77778,0.77778,0.77778,0.77778,
176 0.88575, 0.8988, 0.8378, 0.8029, 0.7876, 0.7805, 0.7799, 0.7801,
177 0.87268, 0.8692,0.8647,0.8479,0.8237,0.7975,0.7881,0.7784,
178 0.85182, 0.8525,0.8366,0.8198,0.8054,0.7903,0.7839,0.782,
179 0.83542, 0.8362,0.8306,0.8196,0.8076,0.7918,0.7842,0.7806,
180 0.82629, 0.8278,0.8252,0.8169,0.8074,0.7916,0.7838,0.7802,
181 0.82299, 0.8249,0.823,0.8165,0.8072,0.7922,0.7839,0.7798,
182 0.82357, 0.8257,0.8241,0.8178,0.8084,0.7927,0.7839,0.7794,
183 0.82657, 0.828,0.8264,0.8199,0.8107,0.7939,0.7842,0.7796,
184 0.8311, 0.8234,0.8295,0.8228,0.8136,0.796,0.7854,0.7798,
185 0.8363, 0.8366,0.8342,0.8267,0.8168,0.7986,0.7864,0.7805,
186 0.84762, 0.8474,0.8438,0.8358,0.825,0.8041,0.7904,0.7822,
187 0.85846, 0.8583,0.853,0.8444,0.8336,0.8118,0.7957,0.7854,
188 0.8684, 0.8674,0.8619,0.8531,0.8423,0.8186,0.8011,0.7898,
189 0.87713, 0.8755,0.8709,0.8616,0.8504,0.8265,0.8072,0.7939,
190 0.88479, 0.8831,0.8779,0.8695,0.8578,0.8338,0.8133,0.799,
191 0.89972, 0.8986,0.8936,0.8846,0.8742,0.8504,0.8294,0.8125,
192 0.91028, 0.9089,0.9043,0.8967,0.8869,0.8649,0.8438,0.8253,
193 0.91793, 0.9166,0.9125,0.9058,0.897,0.8768,0.8557,0.8372,
194 0.92371, 0.9226,0.9189,0.9128,0.905,0.8861,0.8664,0.8484,
195 0.93135, 0.9304,0.9274,0.9226,0.9164,0.9006,0.8833,0.8662,
196 0.93607, 0.9353,0.9329,0.9291,0.924,0.9109,0.8958,0.8802,
197 0.93927, 0.9387,0.9366,0.9334,0.9292,0.9162,0.905,0.8911,
198 0.94149, 0.9409,0.9393,0.9366,0.9331,0.9236,0.9122,0.8997,
199 0.94306, 0.9426,0.9412,0.9388,0.9357,0.9276,0.9175,0.9065,
200 0.94419, 0.9437,0.9425,0.9406,0.938,0.9308,0.9219,0.9119,
201 0.94571, 0.9455,0.9445,0.943,0.9409,0.9353,0.9283,0.9201,
202 0.94662, 0.9464,0.9456,0.9444,0.9428,0.9382,0.9325,0.9258,
203 0.94723, 0.9471,0.9464,0.9455,0.9442,0.9405,0.9355,0.9298,
204 0.94764, 0.9474,0.9469,0.9462,0.945,0.9418,0.9378,0.9328,
205 0.9479, 0.9478,0.9474,0.9465,0.9457,0.943,0.9394,0.9352,
206 0.94827, 0.9481,0.948,0.9472,0.9467,0.9447,0.9422,0.9391,
207 0.94842, 0.9484,0.9481,0.9478,0.9472,0.9458,0.9437,0.9415,
208 0.94852, 0.9484,0.9483,0.948,0.9475,0.9465,0.9449,0.943,
209 0.94861, 0.9487,0.9484,0.9481,0.9479,0.9468,0.9455,0.943,
210 0.94872, 0.9486,0.9486,0.9483,0.9482,0.9475,0.9464,0.9452,
211 0.94881, 0.9488,0.9489,0.949,0.9487,0.9482,0.9476,0.9468,
212 0.94863, 0.9487,0.9489,0.9491,0.9493,0.9491,0.9483,0.9476,
213 0.94444, 0.94444,0.94444,0.94444,0.94444,0.94444,0.94444,0.94444
221 for (
int n = 0; n < 37; n++) {
222 if (tsmin >
tstar[n+1]) {
225 if (tsmax >
tstar[n+1]) {
229 if (m_nmin < 0 || m_nmin >= 36 || m_nmax < 0 || m_nmax > 36) {
235 for (
int i = 0; i < 37; i++) {
237 vector<double> c(DeltaDegree+1);
239 fitDelta(0, i, DeltaDegree, c.data());
240 m_o22poly.push_back(c);
242 fitDelta(1, i, DeltaDegree, c.data());
243 m_apoly.push_back(c);
245 fitDelta(2, i, DeltaDegree, c.data());
246 m_bpoly.push_back(c);
248 fitDelta(3, i, DeltaDegree, c.data());
249 m_cpoly.push_back(c);
253double MMCollisionInt::fitDelta(
int table,
int ntstar,
int degree,
double* c)
274 return polyfit(8, degree, delta, begin, w.data(), c);
277double MMCollisionInt::omega22(
double ts,
double deltastar)
280 for (i = 0; i < 37; i++) {
281 if (ts < tstar22[i]) {
285 int i1 = std::max(i - 1, 0);
291 vector<double> values(3);
292 for (i = i1; i < i2; i++) {
293 if (deltastar == 0.0) {
296 values[i-i1] =
poly6(deltastar, m_o22poly[i].data());
299 return quadInterp(log(ts), &
m_logTemp[i1], values.data());
302double MMCollisionInt::astar(
double ts,
double deltastar)
305 for (i = 0; i < 37; i++)
if (ts < tstar22[i]) {
308 int i1 = std::max(i - 1, 0);
314 vector<double> values(3);
315 for (i = i1; i < i2; i++) {
316 if (deltastar == 0.0) {
319 values[i-i1] =
poly6(deltastar, m_apoly[i].data());
322 return quadInterp(log(ts), &
m_logTemp[i1], values.data());
325double MMCollisionInt::bstar(
double ts,
double deltastar)
328 for (i = 0; i < 37; i++)
if (ts < tstar22[i]) {
331 int i1 = std::max(i - 1, 0);
337 vector<double> values(3);
338 for (i = i1; i < i2; i++) {
339 if (deltastar == 0.0) {
342 values[i-i1] =
poly6(deltastar, m_bpoly[i].data());
345 return quadInterp(log(ts), &
m_logTemp[i1], values.data());
348double MMCollisionInt::cstar(
double ts,
double deltastar)
351 for (i = 0; i < 37; i++)
if (ts < tstar22[i]) {
354 int i1 = std::max(i - 1,0);
360 vector<double> values(3);
361 for (i = i1; i < i2; i++) {
362 if (deltastar == 0.0) {
365 values[i-i1] =
poly6(deltastar, m_cpoly[i].data());
368 return quadInterp(log(ts), &
m_logTemp[i1], values.data());
371void MMCollisionInt::fit_omega22(
int degree,
double deltastar,
double* o22)
373 int n = m_nmax - m_nmin + 1;
374 vector<double> values(n);
377 for (
int i = 0; i < n; i++) {
378 if (deltastar == 0.0) {
381 values[i] =
poly6(deltastar, m_o22poly[i+m_nmin].data());
385 polyfit(n, degree, logT, values.data(), w.data(), o22);
388void MMCollisionInt::fit(
int degree,
double deltastar,
double* a,
double* b,
double* c)
390 int n = m_nmax - m_nmin + 1;
391 vector<double> values(n);
394 for (
int i = 0; i < n; i++) {
395 if (deltastar == 0.0) {
398 values[i] =
poly6(deltastar, m_apoly[i+m_nmin].data());
402 polyfit(n, degree, logT, values.data(), w.data(), a);
404 for (
int i = 0; i < n; i++) {
405 if (deltastar == 0.0) {
408 values[i] =
poly6(deltastar, m_bpoly[i+m_nmin].data());
412 polyfit(n, degree, logT, values.data(), w.data(), b);
414 for (
int i = 0; i < n; i++) {
415 if (deltastar == 0.0) {
418 values[i] =
poly6(deltastar, m_cpoly[i+m_nmin].data());
422 polyfit(n, degree, logT, values.data(), w.data(), c);
Monchick and Mason collision integrals.
void init(double tsmin, double tsmax)
Initialize the object for calculation.
static double astar_table[39 *8]
astar table from MM
static double cstar_table[39 *8]
cstar table from MM
static double tstar[39]
table of tstar values
static double omega22_table[37 *8]
Table of omega22 values from MM.
static double bstar_table[39 *8]
bstar table from MM
vector< double > m_logTemp
Log temp.
This file contains definitions for utility functions and text for modules, inputfiles and logging,...
R poly6(D x, R *c)
Templated evaluation of a polynomial of order 6.
double polyfit(size_t n, size_t deg, const double *xp, const double *yp, const double *wp, double *pp)
Fits a polynomial function to a set of data points.
Namespace for the Cantera kernel.
Contains declarations for string manipulation functions within Cantera.
Various templated functions that carry out common vector and polynomial operations (see Templated Arr...