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A portable framework for high-order spectral element flow simulations
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sigma_nut_kernel.h
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1#ifndef __COMMON_SIGMA_NUT_KERNEL_H__
2#define __COMMON_SIGMA_NUT_KERNEL_H__
3/*
4 Copyright (c) 2024, The Neko Authors
5 All rights reserved.
6
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8 modification, are permitted provided that the following conditions
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10
11 * Redistributions of source code must retain the above copyright
12 notice, this list of conditions and the following disclaimer.
13
14 * Redistributions in binary form must reproduce the above
15 copyright notice, this list of conditions and the following
16 disclaimer in the documentation and/or other materials provided
17 with the distribution.
18
19 * Neither the name of the authors nor the names of its
20 contributors may be used to endorse or promote products derived
21 from this software without specific prior written permission.
22
23 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
24 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
25 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
26 FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
27 COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
28 INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
29 BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
30 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
31 CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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33 ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
34 POSSIBILITY OF SUCH DAMAGE.
35*/
36
40#include <cmath>
41#include <algorithm>
42template< typename T>
43__global__ void sigma_nut_compute(const T * __restrict__ g11,
44 const T * __restrict__ g12,
45 const T * __restrict__ g13,
46 const T * __restrict__ g21,
47 const T * __restrict__ g22,
48 const T * __restrict__ g23,
49 const T * __restrict__ g31,
50 const T * __restrict__ g32,
51 const T * __restrict__ g33,
52 const T * __restrict__ delta,
53 T * __restrict__ nut,
54 const T * __restrict__ mult,
55 const T c,
56 const T eps,
57 const int n){
58
59 const int idx = blockIdx.x * blockDim.x + threadIdx.x;
60 const int str = blockDim.x * gridDim.x;
61
62 T sigG11, sigG12, sigG13, sigG22, sigG23, sigG33;
63 T sigma1, sigma2, sigma3;
64 T Invariant1, Invariant2, Invariant3;
65 T alpha1, alpha2, alpha3;
66 T Dsigma;
67 const T pi_3 = 4.0/3.0*atan(1.0);
68 T tmp1;
69
70 for (int i = idx; i < n; i += str) {
71
72 const T g11_r = g11[i];
73 const T g12_r = g12[i];
74 const T g13_r = g13[i];
75 const T g21_r = g21[i];
76 const T g22_r = g22[i];
77 const T g23_r = g23[i];
78 const T g31_r = g31[i];
79 const T g32_r = g32[i];
80 const T g33_r = g33[i];
81 const T delta_r = delta[i];
82
83 sigG11 = g11_r*g11_r + g21_r*g21_r + g31_r*g31_r;
84 sigG22 = g12_r*g12_r + g22_r*g22_r + g32_r*g32_r;
85 sigG33 = g13_r*g13_r + g23_r*g23_r + g33_r*g33_r;
86 sigG12 = g11_r*g12_r + \
87 g21_r*g22_r + \
88 g31_r*g32_r;
89 sigG13 = g11_r*g13_r + \
90 g21_r*g23_r + \
91 g31_r*g33_r;
92 sigG23 = g12_r*g13_r + \
93 g22_r*g23_r + \
94 g32_r*g33_r;
95
96 if (abs(sigG11) < eps) {
97 sigG11 = 0.0;
98 }
99 if (abs(sigG12) < eps) {
100 sigG12 = 0.0;
101 }
102 if (abs(sigG13) < eps) {
103 sigG13 = 0.0;
104 }
105 if (abs(sigG22) < eps) {
106 sigG22 = 0.0;
107 }
108 if (abs(sigG23) < eps) {
109 sigG23 = 0.0;
110 }
111 if (abs(sigG33) < eps) {
112 sigG33 = 0.0;
113 }
114
115 if (abs(sigG12*sigG12 + \
116 sigG13*sigG13 + sigG23*sigG23) < eps) {
117 sigma1 = sqrt(max(max(max(sigG11, sigG22), sigG33), 0.0));
118 sigma3 = sqrt(max(min(min(sigG11, sigG22), sigG33), 0.0));
119 Invariant1 = sigG11 + sigG22 + sigG33;
120 sigma2 = sqrt(abs(Invariant1 - sigma1*sigma1 - sigma3*sigma3));
121 } else {
122 Invariant1 = sigG11 + sigG22 + sigG33;
123 Invariant2 = sigG11*sigG22 + sigG11*sigG33 + sigG22*sigG33 - \
124 (sigG12*sigG12 + sigG13*sigG13 + sigG23*sigG23);
125 Invariant3 = sigG11*sigG22*sigG33 + \
126 2.0*sigG12*sigG13*sigG23 - \
127 (sigG11*sigG23*sigG23 + sigG22*sigG13*sigG13 + \
128 sigG33*sigG12*sigG12);
129
130 Invariant1 = max(Invariant1, 0.0);
131 Invariant2 = max(Invariant2, 0.0);
132 Invariant3 = max(Invariant3, 0.0);
133
134 alpha1 = Invariant1*Invariant1/9.0 - Invariant2/3.0;
135
136 alpha1 = max(alpha1, 0.0);
137
138 alpha2 = Invariant1*Invariant1*Invariant1/27.0 - \
139 Invariant1*Invariant2/6.0 + Invariant3/2.0;
140
141 tmp1 = alpha2/sqrt(alpha1 * alpha1 * alpha1);
142
143 if (tmp1 <= -1.0) {
144 sigma1 = sqrt(max(Invariant1/3.0 + sqrt(alpha1), 0.0));
145 sigma2 = sigma1;
146 sigma3 = sqrt(Invariant1/3.0 - 2.0*sqrt(alpha1));
147
148 } else if (tmp1 >= 1.0) {
149 sigma1 = sqrt(max(Invariant1/3.0 + 2.0*sqrt(alpha1), 0.0));
150 sigma2 = sqrt(Invariant1/3.0 - sqrt(alpha1));
151 sigma3 = sigma2;
152
153 } else {
154 alpha3 = acos(tmp1)/3.0;
155
156 if (abs(Invariant3) < eps) {
157 sigma1 = sqrt(max(Invariant1/3.0 + \
158 2.0*sqrt(alpha1)*cos(alpha3), 0.0));
159 sigma2 = sqrt(abs(Invariant1 - sigma1*sigma1));
160 sigma3 = 0.0;
161 } else {
162 sigma1 = sqrt(max(Invariant1/3.0 + \
163 2.0*sqrt(alpha1)*cos(alpha3), 0.0));
164 sigma2 = sqrt(Invariant1/3.0 - \
165 2.0*sqrt(alpha1)*cos(pi_3 + alpha3));
166 sigma3 = sqrt(abs(Invariant1 - \
167 sigma1*sigma1-sigma2*sigma2));
168 }
169 }
170 }
171
172 if (sigma1 > 0.0) {
173 Dsigma = sigma3*(sigma1 - sigma2)*(sigma2 - sigma3)/(sigma1*sigma1);
174 } else {
175 Dsigma = 0.0;
176 }
177
178 Dsigma = max(Dsigma, 0.0);
179
180 nut[i] = (c*delta_r)*(c*delta_r) * Dsigma * mult[i];
181 }
182}
183#endif // __COMMON_SIGMA_NUT_KERNEL_H__
i
const int i
Definition ax_helm_full_kernel.h:95
dirichlet_apply_scalar_kernel
__global__ void dirichlet_apply_scalar_kernel(const int *__restrict__ msk, T *__restrict__ x, const T g, const int m)
Definition dirichlet_kernel.h:42
sigma_nut_compute
__global__ void sigma_nut_compute(const T *__restrict__ g11, const T *__restrict__ g12, const T *__restrict__ g13, const T *__restrict__ g21, const T *__restrict__ g22, const T *__restrict__ g23, const T *__restrict__ g31, const T *__restrict__ g32, const T *__restrict__ g33, const T *__restrict__ delta, T *__restrict__ nut, const T *__restrict__ mult, const T c, const T eps, const int n)
Definition sigma_nut_kernel.h:43
g23
__global__ void const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ g23
Definition ax_helm_kernel.h:161
g22
__global__ void const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ g22
Definition ax_helm_kernel.h:157
g13
__global__ void const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ g13
Definition ax_helm_kernel.h:160
g12
__global__ void const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ g12
Definition ax_helm_kernel.h:159
g33
__global__ void const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ g33
Definition ax_helm_kernel.h:158
g11
__global__ void const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ const T *__restrict__ g11
Definition ax_helm_kernel.h:156
max
#define max(a, b)
Definition tensor.cu:40